Are Crises Predictable? A Review of the Early Warning Systems in Currency and Stock Markets
AAre Crises Predictable? An Review of the Early Warning Systemsin the Currency and Stock Markets
Peiwan Wang a,b , Lu Zong a,b, ∗ a Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University. b
111 Ren’ai Road, Dushu Lake Science and Education Innovation District, Suzhou Industrial Park, Suzhou, Jiangsu Province,P.R. China, 215123.
Abstract
The study efforts to explore and extend the crisis predictability by synthetically reviewing and comparing afull mixture of early warning models into two constitutions: crisis identifications and predictive models. Givenempirical results on Chinese currency and stock markets, three-strata findings are concluded as (i) the SWARCHmodel conditional on an elastic thresholding methodology can most accurately classify crisis observations andgreatly contribute to boosting the predicting precision, (ii) stylized machine learning models are preferred givenhigher precision in predicting and greater benefit in practicing, (iii) leading factors sign the crisis in a diversifiedway for different types of markets and varied prediction periods.
1. Introduction
The predictability of financial crises is a continually debating open question and yet settled through trans-centuries’ arguments among economists and practitioners. The core of controversies focuses on whether thecrisis is triggered by unexpected exogenous factors or the market endogenous instability. According to theclassic Efficient Market Hypothesis (EMH) theory that is proposed by Malkiel and Fama in 70’s of last century,the securities prices in an ideal market can fully reflect all available information and the financial crises occuras long as external shocks, known as the ‘black swan’ factors, arise. In that situation, governors can contributelittle to minimize the economic losses after the crisis. Malkiel and Fama (1970)’ theory shows strong assumptionon human behaviours’ rationality, however market participants are hardly to be always rational and quicklyrespond to market information in practice. Arthur (1999) then relax the strong assumption by pointing out theevolution process of the economy is dynamic, nonlinear and uncertain, which also inherently coincides to Schiller(2000)’s revolutionary proposal of the market endogenous imperfection being mainly induced by the irrationalfactors. In fact, the essence of this argument fertilizes the flourishing studies on financial crisis forecastingsystem development as the theoretic basis renders inclination to dilute the assertion that crisis is randomlyunpredictable. Sornette (2009) formally advocates the argument that crises are predictable, as the studyannounced, the crisis is the ‘dragon-king’, not the unpredictable ‘black swan’, since before the crisis abruptlybursts, precursory symptoms like substantial outliers, will be teeming observed in reality. It is inspiring toacknowledge the crisis predictability with a positive attitude given a series of rigorous statistical test on predictedresults, even though yet deliver 100% trust. EMH (Malkiel and Fama, 1970) and ‘dragon-king’ (Arthur, 1999;Schiller, 2000; Sornette, 2009) holders, they both admit the fact that perfectly grasping the exact time of crisesseems less attainable, but gaining the awareness on precursory signals of potential financial shocking in advanceis achievable.
The disputes between two against arguing mainstreams are yet settled, particularly in the contemporary datascience background, academics and practitioners have ignited a great volume of diligent works on developingearly warning systems to back up the precursory evidence before crisis shocking occurs. The first generationof crisis prediction studies started up in the late 1990’s, which concentrates to apply the economic models ∗ Corresponding author
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[email protected] (Lu Zong)
Preprint submitted to Elsevier October 21, 2020 a r X i v : . [ q -f i n . M F ] O c t nd statistical approaches (Eichengreen et al., 1995; Frankel and Rose, 1996; Patel and Sarkar, 1998; Bergand Pattillo, 1999b; Kaminsky and Reinhart, 1999; Kaminsky et al., 1998) to forecast nationwide bankingand currency crises. The vulnerability of crisis may cannot be convincingly revealed by first generation ofmodels cluster, as IMF published paper (Berg and Pattillo, 1999a) summarized and exercised on the 1997 Asiancurrency crisis, their predicting power is barely satisfactory unless under plausible modifications. Machinelearning techniques (Nag and Mitra, 1999; Oh et al., 2006; Celik and Karatepe, 2007) are then locked toconstruct the second generation of early warning systems considering its specialization on predicting big sizenon-linear data. The impetus brought by these state-of-art models accelerates the progress of predicting financialcrises in the data driven situation (Holopainen and Sarlin, 2017; Beutel et al., 2019), albeit gives concessionsto the interpretable expressiveness on detecting leading crisis factors. In general, there are three layers ofabsences in both first and second generations of crisis predicting model. First, most studies identify the crisisobservations on the single index with an arbitrary cutoff, that lacks the elasticity as the back-forward lookinghistoric sample horizons are varied. Second, the good-of-fitness evaluation is either deficient or ambiguous onmarking the leading time, such as Bussiere and Fratzscher (2006); Sevim et al. (2014) estimate the probabilityof crisis occurring within a future horizon interval to soothe the pain of matching to exact crashing time point(this is actually the case of omission for measuring leading time), Kaminsky et al. (1998); Dawood et al. (2017)state each leading factors that contribute to the crisis warning thus the leading period is given by countingthe periods of leading indicators in advance of the first crisis signal occurs (there are a series of factors leadingtime), and Kim et al. (2004); Oh et al. (2006) directly chronicles the crashing event and the produced signalinglevels to visualize how the output precedes to the true crises (impacting but not applicable to high-frequencyand long-horizon data). Last, the developed predicting system is rarely assessed in practice. Specifically, it isindispensable to test whether the investors’ wealth will be gained as the crisis forecasting system participates.A board scope of theoretical and experimental research studies on either developing crisis predictive modelsor investigating leading economic factors for a wide range of countries in various development situations, suchas developed ,developing, emerging, and low-income countries (Frankel and Rose, 1996; Demirg¨u¸c-Kunt andDetragiache, 1998; Koyuncugil and Ozgulbas, 2012; Babeck´y et al., 2013; Kim et al., 2020) have been explored byscholars and practitioners. For policymakers, institutional researchers and public investors, to have a competentearly warning system (EWS) to forewarn the crisis, is equivalent to grasp the opportunity to counter the risksthat potentially lead destructive damaging as well as to make the economy vigorously circulating and the societycomfortably steady-going. Thus, how to distinguish robust EWS model among a great quantity of qualifiedmodels based on prominent predictive models seems more than momentous. In fact, the horse race amongEWS models (Holopainen and Sarlin, 2017) that predict either macroscopic economic crises or market-specificturbulence, has never been suspended, especially in comparing the merits and shortages between the classicregression models and stylized machine learning techniques. Sevim et al. (2014) compare the EWS modelsdeveloped with binary logistic regressions and machine learning techniques of artificial neural networks (ANN)and decision trees to predict the Turkish currency crisis and accredit that both decision supporting models andANNs superior to the traditional regression models. The against conservative opinion, as Beutel et al. (2019)which systematically examine the out-of-sample performance for almost full series of proposed EWS modelshold, deems that the conventional logit regression is fairly efficient to predict systematic banking crises, machinelearning based EWS models however need more enhancements before being fully granted in real-world prediction.Such comparison studies, though predicting models are categorized and uniformly verified, yet comprehensivelydiscuss the varied crisis definitions but thetically adopt one classifier for harmonizing comparison metrics inconvenience. Therefore, to fully explore the comparative EWS models, various combinations of different typesof classifiers and predictive models are required to be implemented and investigated. Our aim is not either to advocate the EWS predicting as mythological oracle or to investigate all proposedEWS models with a overloaded ambition. We effort to preen the pending issues in comparative EWS modelswith the hope to inspire further exploring sparkles for subsequent researches. To implement this goal, wespecify candidate EWS models that will be compared in a unified frameworks with two partitioned constituentsto sensibly reason their potentials in addressing crisis identification and warning signal production challenges.In addition to use the chronology critical events, we novelly boostrap the classified samples and calculate theaverage misspecification rates to reveal the classifier performance in an statistically objective way. To supportthe investors render better verdicts in a credible and operational way, we propose the EWS participated portfolioconstructing process and compare the Sharpe ratios and CER values under varied aversion levels.The study will be explored in the following sequence. Section 2 will review and summarize the EWS models interms of crisis classification techniques, predictive models, performance measurements and variable contributing2egree estimation. Section 3 shows the empirical results of examining EWS models on Chinese currency andstock markets in terms of classified crisis observations, model predicting robustness and detected leading crisisfactors respectively. Section 4 will conclude the compared results and key implications, as well as give furthersuggestion and discussion.
2. Methodology Reviews
Main concerns for developing EWS models embody into two aspects, that respective pros and cons are yetsystematically reviewed in terms of structural components of (1) the identification techniques for labelling crisisobservations with data frequency variations , and (2) the predictive models’ forecasting power of producingwarning signals in a unified measurement frameworks.The current developed EWS models are mainly designed for two types of financial crisis: the crisis thatconcerns the systematic risks, such as the banking crisis and the debt crisis, and the market specific crisis thatrelates more to iconic price or index dynamics’ turbulences, such as the currency and stock market crashes.The classification for first type of crisis gravely relies on central bank’s reports, financial institution researchpublications and experts’ opinions (Demirg¨u¸c-Kunt and Detragiache, 1998; Kaminsky and Reinhart, 1999;Lestano et al., 2004; Beckmann, 2007; Celik and Karatepe, 2007; Davis and Karim, 2008; Reinhart and Rogoff,2011; Dawood et al., 2017), which data are either difficult to quantized (Davis and Karim, 2008) or costly toaccess for the public. Otherwise, the market specific crisis dating technique that commonly labels the crisislevel of the market price index or the technically quantized price index (TQI) , such as the exchange marketpressure index ( ? Patel and Sarkar, 1998; Lestano et al., 2004; Peng and Bajona, 2008; Yu et al., 2010; Sevimet al., 2014) and the market instability index (Kim et al., 2009; Yoon and Park, 2014; Li et al., 2015; Chatziset al., 2018) are more accessible and processable.The TQI classifier is though popular for market crisis studies, generally puzzled by the crisis cutoff de-termination, in other words, the value of threshold to produce crisis observations is either crudely imposed aarbitrary value (or a fixed percentile) or mildly taken the mean plus a factor of standard deviations, which failsto dynamically adapt to the crisis severity level in different market turbulence scenarios. An alternative pathto classify the market specific crisis is in virtue of the Markovian switching regime model, which first clustersobservations into several leveled (for example, low- and high-) volatility states and then recognizes crises bytaking (conventionally) the top half of the filtering probability for high-volatility state (Hamilton and Susmel,1994; Hamilton and Gang, 1996; Abiad, 2007). The gap of cutoff optimization is further bridged accordingto the market turmoil level variation by imposing an automatically thresholding approach on the two-peakmethodology theoretical basis (Rosenfeld and Torre, 1983; Ohtsu, 2007) on the SWARCH classifier. This dy-namically adaptive classifier has been successfully verified in predicting stock crashes (Wang et al., 2020a). Theother issue that is rarely mentioned in previous studies for EWS classifier construction is the variation of datafrequency. The crisis observed on low frequently distributed data, such as monthly, quarterly and annuallydata, includes the pre-crisis effect into the crisis binary dependent variable definition (Bussiere and Fratzscher,2006; Sevim et al., 2014; Candelon et al., 2014), which is reasonable to instruct the long term macro-economicpolicy adjustments, but yet suitable to direct short term investment portfolio improvement. While, for dailydata, to imitate the timeliness in real trading scenarios, it seems more reasonable to eliminate the pre-crisiseffect from the crisis variable definition. Except the issue of determining ‘true’ crisis labels, how to validate theclassifier’s credibility is alike pended, specifically, the way of listing the chronology of historic crisis events orsignificant turning point for crises against the classifiers’ dated crisis episodes (Oh et al., 2006; Abiad, 2007)lacks of statistical persuasion. In the study, a more logical validation approach will be proposed to examine theclassifier’s performance besides the chronological table list.The predictive models that support EWS constructions will be clustered as three main branches: thelogit/probit regression model - which classic methodology pioneers the EWS construction and keeps mostprevailing in the crisis prediction studies (Eichengreen et al., 1995; Frankel and Rose, 1996; Berg and Pattillo,1999b; Bussiere and Fratzscher, 2006; Candelon et al., 2014; Dawood et al., 2017); the indicator approach -which provides an alternative nonparametric methodology to detect the leading factors and uses the refinedfactors to construct the crisis indicator (Kaminsky et al., 1998; Kaminsky and Reinhart, 1999; Lestano et al.,2004; Berg et al., 2005; Coudert and Gex, 2008; Reinhart and Rogoff, 2011, 2013; Peng and Bajona, 2008);the state-of-art machine learning and deep learning models (Nag and Mitra, 1999; Oh et al., 2006; Celik andKaratepe, 2007; Yu et al., 2010; Yoon and Park, 2014; Chatzis et al., 2018; Beutel et al., 2019; Wang et al., To the best of our knowledge, most studies yet clearly pinpoint how data frequency effect the EWS model performance. TQI is commonly a composite of weighing several market price index factors.
Eichengreen et al. (1995), Frankel and Rose (1996) and Kaminsky et al. (1998) almost simultaneously proposethe concept of EWS for currency crisis prediction. To quantize the crisis variable into binary case for zero andone, the market pressure index of
EP I is defined. Specifically, the formula for
EP I are different in Eichengreenet al. (1995) and Kaminsky et al. (1998), which are denoted as
EP I
ERW and
EP I
KLR in the following formulaerespectively.
EP I
ERW = 1 σ e ∆ e t e t − σ r ( ∆ rm t rm t − ∆ rm US,t rm US,t ) + 1 σ i ∆( i t − i US,t ) (1)
EP I
KLR = ∆ e t e t − σ e σ r ∆ r t r t + σ e σ i ∆ u t , (2) e t denotes the currency exchange rate per US dollars and ∆ e t e t is the relative change in the exchange rate. σ e is the standard deviation for ∆ e t e t . Since the US is the reference country for EP I
ERW construction, ( ∆ rm t rm t − ∆ rm US,t rm US,t ) and σ r are the difference between the relative change in the ratio of foreign reserves and M1 and thereference country and its standard deviation respectively. σ i is the standard deviation of nominal interest ratedifferential of ∆( i t − i US,t ). In the
EP I
KLR , e t , ∆ e t and σ e keep same as EP I
ERW . σ r denotes the standarddeviation of the relative change in the gross foreign reserves ∆ r t r t and σ i denotes the standard deviation for thenominal interest rate change ∆ i t .Lestano et al. (2004) and Lestano (2007) then further compare the sensitivity of dating currency crisis underbetween EP I
ERW (Eichengreen et al., 1995) and
EP I
KLR (Kaminsky et al., 1998) to different thresholds byvarying the value of λ , and find the EP I
KLR is the preferred index with higher sensitivity. Sevim et al. (2014)validates the conclusion and further proposes a more concise index of financial pressure index (
F P I ) to measurethe currency crisis in a standardized average among gross foreign exchange reserves, exchange rate and interestrate, which reasonably synthesizes domestic currency and expels the dispute of choosing the reference country.
F P I t = 13 ( e t − µ e σ e − r t − µ r σ r + i t − µ i σ i ) , (3)where e t , r t and i t are the percentage changes in the exchange rate, monthly gross foreign exchange reservesand monthly change of overnight interest rates at time t , respectively. µ (cid:48) s and σ (cid:48) s are the mean and standarddeviation value for each accounted terms.The crisis variable, in our study, thus will be constructed by hiring the binary function of C t = (cid:40) , if F P I t > µ F P I + λ fpi σ F P I , otherwise. (4) µ F P I and σ F P I are the mean and standard deviation for the FPI, and λ is the coefficient to control the boundto classify crisis observations.One of the top cited study of Bussiere and Fratzscher (2006), greatly contributes to specify the crisisvariable including either the pre-crisis effect or both of the pre-crisis and post-crisis effect, in other words,the binary forward-looking or the ternary forward- and backward-looking variable will be defined to grasp the4risis information in a fixed window of future and past period to rationalize the goal of predicting ‘whether acrisis occurs within a specific time horizon’ and fixing ‘post-crisis bias that fails to distinguish between tranquilperiods and recovery periods’. For the long-term predicting system, the post-crisis bias effect, however, keepscontroversial in EWS studies since the crisis variable that covers the sustainable impact distracts the goal ofearly notifying warning signals. In the study, the binary case which is same defined as Bussiere and Fratzscher(2006) will be adopted for allowing the general comparisons with other binary classified models (Berg andPattillo, 1999b; Lestano et al., 2004; Abiad, 2007; Davis and Karim, 2008; Sevim et al., 2014). The definitionis listed as follows. Y t = (cid:40) ∃ k = 0 , ..., s.t. C t + k = 1 , t within the past rolling window size of m . CM AX t = P t max ( P t , ..., P t − m ) (6) P t is the price index at time t . The binary crisis variable for short-term will be similarly defined as follows andthe ‘perfect signaling’ variable for long-term keeps the same with equation (2.1.1). C t = (cid:40) , if CM AX t ≤ µ CMAX − λ cmx σ CMAX , otherwise. (7)As Table 1 lists, the upper panel shows calculating formulae for classic TQI defined crisis variables. Inthis study, to make the classifier generally comparable, the TQI of F P I and
CM AX will not use the ad-hocthresholding coefficient λ fpi = 3 and λ cmx = 2 . An flexible alternative to define the crisis by distinguishing the volatility state between tranquil and turmoilperiods is inspired by Hamilton and Susmel (1994), which study proposes the SWARCH model to project themarket turmoil level in the business cycle by first clustering the (price) index into different regimes/states andthen inferring the probability of observations staying in high-volatility state. Its robustness in financial crisis andcontagion detections have been further studied and verified (Ramchand and Susmel, 1998; Edwards and Susmel,2001; BenSa¨ıda, 2018; Wang and Zong, 2019). IMF has (Abiad, 2007) straightforward adopted the SWARCHto predict the currency crisis in Asian countries, which intrinsically defines the crisis dependent variable basedon half cutting the filtering probability for high-volatility state (that will be referred as
F P H in the followingcontent). Given consistency of conserving the pre-crisis effect for long-term prediction, Abiad (2007) similarlydefines a ‘perfect signal variable’ to indulge a 12 months window length for long-term forecasting. Table 2shows the long-term dependent variable Y t based SWARCH as an equivalent transformation of the short-termforecasting .In the study, we adopted AR(p)-SWARCH(K,q) model to classify the stock and currency price index volatil-ity. y t = u + θ y t − + θ y t − + · · · + θ p y t − p + (cid:15) t , (cid:15) t |I t − ∼ N (0 , h t ); (8) h t γ s t = α + α (cid:15) t − γ s t − + · · · + α q (cid:15) t − q γ s t − q , s t = { , . . . , K } . (9) (cid:15) t is normally distributed error term with variance of h t . α (cid:48) s are non-negative coefficients for modeling scaledvariance term, γ (cid:48) s are scaling parameters relating to the state-dependent variable s t . There are K regimes for The rolling window size is customarily equal to 24. In our study, the lengthy window however will result in unexpectedinformation loss, hence shorter length of 12 will be substituted The deriving process of the transformed equivalence is referred to Abiad (2007). It constructs on the imposed assumption ofthe crisis probability in the future months will be neither worsen or improved. a b l e : T h e t a b l e s u mm a r i ze s c r i s i s d a t i n g m e t h o d o l og i e s . C l a ss i fi e r M a r k e t I nd e x F o r m u l a S o u r c e d r e f e r e n c e T Q I c u rr e n c y E P I C a i , t = i f %∆ e b i , t > % F r a n k e l a nd R o s e ( ) a nd %∆ e i , t > ( % + %∆ e i , t − ) C i , t = i f E P I i , t > µ c E P I t + σ c E P I t E i c h e n g r ee n e t a l. ( ) C i , t = i f E P I i , t > µ E P I t + σ E P I t K a m i n s ky e t a l. ( ) Y d i , t = i f ∃ k = ,..., s . t . C i , t + k = B u ss i e r e a nd F r a t z s c h e r ( ) Y i , t = i f ∃ k = ,..., p s . t . C i , t − k = C e i , t = i f K L R m f i , t > µ K L R m t + σ K L R m t C a nd e l o n e t a l. ( ) C i , t = i f (cid:80) j = C i , t + j > c u rr e n c y FP I K t = i f FP I t > µ F P I t + σ F P I t S e v i m e t a l. ( ) P S t = i f ∃ k = ,..., s . t . K t + k = s t o c k C M A X CC t = i f C M A X t ≤ µ C M A X t − . σ C M A X t L i e t a l. ( ) Y t = i f ∃ k = ,..., s . t . CC t + k = Y t = i f ∃ k = ,..., s . t . CC t − k = S W A R C H s t o c k FP H g C t = i f FP H t > . H a m il t o n a ndSu s m e l ( ) C t = i f FP H t > c , W a n g e t a l. ( ) w h e r e c i s t h e t w o - p e a k m e t h o d o p t i m i z e d c u t o ff v a l u e . c u rr e n c y C t = i f − ( − FP H t ) > . , A b i a d ( ) w h e r e i s t h e l e n g t h o f p r e d i c t i v e m o n t h s . a C i , t i s t h ec r i s i s v a r i a b l e f o r c o un t r y i a tt i m e t . b %∆ e i , t d e n o t e s t h e n o m i n a l d e p r ec i a t i o n o f t h ec u rr e n c y f o r c o un t r y i i n t h e p e r i o d t . c µ a nd σ i s t h e m e a n a nd s t a nd a r dd e v i a t i o n o f t h e d e fin e d i nd e x . d Y i , t i s t h e l oo k - f o r w a r d i n g d e p e nd e n t v a r i a b l e w i t h m o r e t h a n t w o v a l u e s o f ( f o r n o n - c r i s e s ) a nd ( f o r c r i s e s ) b e i n g p r o p o s e d f o r s o l v i n g t h e po s t - c r i s i s b i a s . e C i , t i ss a m e w i t h C i , t a nd C i , t d e fin e s t h ec r i s i s du mm yv a r i a b l ec o nd i t i o n i n go n a t l e a s t o n ec r i s i s i n t h e f o ll o w i n g s i x m o n t h s a pp e a r s , w h i c hp r o p o s e s t h e f o r w a r d l oo k i n g c o n ce p tt o d e fin ec r i s i s v a r i a b l e . f K L R m i s t h e m o d i fi e d K L R p r e ss u r e i nd e x , a nd i s f o r m u l a t e d a s K L R m i , t = ∆ e i , t e i , t − σ e σ r ∆ r i , t r i , t + σ e σ i ∆ i i , t . Sp ec i fi c n o t a t i o n s i n t h e f o r m u l a c a nb e f o und i n C a nd e l o n e t a l. ( ) . g F P H t = fi l t e r i n g p r o b a b i l i t y f o r h i g h - v o l a t i l i t y s t a t e f o r t i m e t . able 2: The table clarifies crisis dating formulae for currency and stock markets. classifier market perfect signal variable crisis variableTQI currency Y t = 1 if ∃ k = 1 , .., C t = 1 if F P I t > µ FPI t + λ fpi σ FPI t s.t. C t + k = 1stock C t = 1 if CMAX t ≤ µ CMAX t − λ cmx σ CMAX t currencySWARCH Y t = 1 if 1 − (1 − F P H t ) > . C t = 1 if F P H t > . pk opt Y t = 1 if 1 − (1 − F P H t ) > c opt , C t = 1 if F P H t > c opt stock s t to present the index volatility states, and the count of regimes is determined by the value of RCM (Angand Bekaert, 2002; Wang et al., 2020b), which metric is proven effective to decide the most suitable value fordistinguishing the volatility state.The filtering probability for high-volatility state (FPH) that is inferred from historic observations Y t can bewritten as follows P ( s t = high-vol. | Y t ; θ t ) , (10) θ t is the parameter vector to be estimated. The crisis variable is henceforth defined as C t = (cid:40) , P ( s t = high-vol. | Y t ; θ t ) ≥ . , otherwise. (11)For long-term horizon prediction, we follow the definition in Abiad (2007) as Y t = (cid:40) , − (1 − P ( s t = high-vol. | Y t ; θ t )) ≥ . , otherwise. (12) The arbitrary cutoff in SWARCH classifier has been further improved with greater robustness in Wang et al.(2020a), that achieves dynamically identifying stock market turbulences by recursively applying the two-peakmethod (Rosenfeld and Torre, 1983; Ohtsu, 2007) to each newly included segment of observations to detectthe valley bottom point as the optimal cutoff value in the forward moving estimation process . In our study,to justify the newly proposed SWARCH classifier on the two-peak method thresholding basis performance oncurrency market, the study will implement both SWARCH classifiers thereafter.The two-peak method is first proposed and applied to distinguish the difference between the object and thebackground grey pixels (Prewitt and Mendelsohn, 1966) by locating the frequency density histogram cancavity(Rosenfeld and Torre, 1983; Weszka, 1978). The optimizing process of the cutoff value for producing crisesis thus inspired by recursively applying the two-peak method to the SWARCH filtering probabilities for thehigh-volatility state i.e. P ( s t = high-vol. | Y t ; ˆ θ t ) as expanding the time horizon from t = l to t = T , where l isthe fixed window size and T is the full sample size. As the example Figure 1 shows, the orange density histogramis plotted for filtering probabilities of high-volatility state, then the concavity of histogram is detected at c = α ,thus α is the optimized cutoff for this time slice. A series of cutoff values will be produced as the time sliceobservations move forward, that means, the crises will be adaptive to a new cutoff as the volatility informationdynamically changes. The algorithm has been specified in Wang et al. (2020a). igure 1: Illustrating the two-peak thresholding methodology: density histogram plot and the concavity detection for optimizingthe cutoff value. The binary crisis variable is thus similarly defined as C t = (cid:40) , P ( s t = high-vol. | Y t ; θ t ) ≥ c optt , otherwise. (13)For long-term horizon prediction, the crisis formula is written as Y t = (cid:40) , − (1 − P ( s t = high-vol. | Y t ; θ t )) ≥ c optt , otherwise. (14)where c optt is the two-peak optimized cutoff value for time t . Logistic regression is one of most toiling econometric models that is empirically used to construct EWSfor predicting curency crisis(Eichengreen et al., 1995; Frankel and Rose, 1996; Bussiere and Fratzscher, 2006),debt crisis (Dawood et al., 2017) and financial crisis based on market index and option (Li et al., 2015). Theadvantage of logit regression model sticks two benefits: the latent assupmtion that the dependent variable islinearly linked to other explanatory variables by adding a logistically distributed error, can distinctly convey therelationship among variables and explain the model uncertainty; on the other side, coefficients (with p-value of t-test) magnify the model interpretability and reliability in discovering influential factors. To mitigating the curseof dimensionality in regressing large explanatory variables on one dependent variable, we adopt the stepwiseregression to extract and retain the effective combination of variables that maximally explain the dependentvariable variation. As mentioned in Beutel et al. (2019), the fixed effect will be removed from the regressionsince it should be more comparable to other predictive models without extra terms. The Logit regression formodeling the probability of binary crisis variable y t at time t ∈ { , ..., T } can be formulated as follows, P r ( y t = 1) = e x t β e x t β , (15)where the x t is the vector of explanatory variables at time t , β is the vector of coefficients. Coefficients will beobtained by maximum likelihood estimation and the joint log likelihood function is written as logL = T (cid:88) t =1 ( y t log ( P r ( y t = 1)) + (1 − y t ) log (1 − P r ( y t = 1))) . (16)In the stepwise backward algorithm, assumed m is the dimension of parameter vector, following steps will beattempted to search for the optimal model.1. Establish the regression model between y and all explanatory variables of x = { x , x , ..., x m } , and do F − test for each x , take the minimum as F l = min { F , F , ..., F m } .2. If F l > F α (1 , T − m +1), no variable will be eliminated, the regression model is the optimal one. Otherwise,we elminate x l and denote the rest of variables as x − l = { x , x , ..., x m − } .8. Establish the regression model between y and x − l , again do the F − test for each x and take the minimumas F l = min { F , F , ..., F m − } .4. If F l > F α (1 , ( T − m + 1) − x l and repeatthe steps of F − test, comparing minimum with the margin and elimination, till not further variable iseliminated from the regression.In general, the backward stepwise first put all variables into the model, and then attempt to remove onevariable to examine whether significant change appears after the elimination. If there is no significant change,this elimination will be retained until all factors that lead significant change to the model are left. Thus,explanatory variables will be eliminated in turn and finally reordered according to their contribution degree tothe model from small to large. KLR indicator approach is introduced in Kaminsky et al. (1998) on the basis of nonparametric methodology,which also stands out in the EWS developing realm as this signal extraction approach not only directly assessesthe abnormality of single variable behaviour before or during the crisis period without the linearity assumptionconstraint, but provides a more comprehensive way to policy makers without training background of econometricand statistical modelling as well (Kaminsky and Reinhart, 1999; Lestano et al., 2004; Davis and Karim, 2008;Peng and Bajona, 2008), even though in the EWS model comparison study of Berg et al. (2005) and Davis andKarim (2008), the improved logit regression is proven to perform better than the signal extraction approachfor predicting currency and banking crises. The approach monitors economic variables in a specified periodand detects the ones deviates from the noise-to-signal ratio (NSR) minimized threshold as leading factors. Thefactors that are detected to anticipate the crisis will be counted into constructing the composite indicator byweighing each variable by their respective inverse of NSR (Kaminsky and Reinhart, 1999; Davis and Karim,2008). The implementing process of KLR methodology is presented as a flowchart diagram, i.e. Figure 2, tosimplify words described steps in a more concise way. Table 3: Confusing table for calculating the noise-to-signal ratio for each cutoff.
Crisis No crisisSignal was issued A BNo signal was issued C DIn the diagram, we first take 80% to 90% percentile of observations for each variable and gradient searchthe optimal cutoff by producing the confusing matrix, as Table 3 shows, calculating (adjusted) noise-to-signalratio (NSR) of B/ ( B + D ) A/ ( A + C ) , and searching for the minimal NSR corresponding cutoff value. Then, factor variableswill be sifted by the extracted minimal NSR of NSR jmin and the optimized cutoff of cutoff jopt for variable X j .As green blocks label in the diagram, two decision conditions are (1) whether the variable value is greater thanthe optimized cutoff and (2) whether the noise-to-signal ratio is smaller than 0.75 . Then condition filtered m out of n factor variables will be synthesized by assigning the corresponding inverse of NSR min as their weightsto compose the final output, normalized crisis indicator of I ct . Machine learning models are the state-of-art techniques that are more flexible than traditional econometricmodels to predict on complex data with non-linearity. A wide range of EWS models constructed on machinelearning techniques, such as neural networks (Nag and Mitra, 1999; Oh et al., 2006; Celik and Karatepe, 2007;Dong et al., 2009; Sevim et al., 2014; Yoon and Park, 2014), decision trees (Tanaka et al., 2016; Samitas et al.,2020; Holopainen and Sarlin, 2017), support vector machine (Ahn et al., 2011), and deep neural networks (Wanget al., 2020a,b), have been studied. According to former comparison work (Beutel et al., 2019; Chatzis et al.,2018) and our previous studies on stock and bond markets (Wang et al., 2020a,b), we select the neural networks,the tree model of random forest and gradient boost and the attention based long-short term memory networksas the candidate machine learning models, to explore deeper comparisons as well as to cover our precedingoutstanding work. Both study adopt the multivariate logit regression. The significant level could be varied for specific markets according to the range of NSR values. Some studies (Davis and Karim,2008) use 0.5 but find the strict value lead none of factors can be drawn as leading factors. { X jt,j = { , ,...,n } ,t = { , ,...,T } } Take 80% - 90% percentile as cutoffsProduce confusing matrix and calculate NSR under each cutoffOutput the NSR jmin and corresponding cutoff jopt (1) | X jt | > | cutoff jopt | ? S jt = 1 S jt = 0 (2) NSR jmin < . ω j = ( N SR jmin ) − ω j = N A
Calculate I ct = (cid:80) mj =1 ω j S jt Output the normalized I ct EndYes No Yes No
Figure 2: Diagram of implementing the KLR signal extraction approach. NSR jmin and cutoff jopt are minimal noise-to-signal ratioand corresponding optimal cutoff for input variable j . I ct is the composite crisis indicator (Kaminsky and Reinhart, 1999). Neural Networks.
As the booming computational vision and big data science unseal a nova technologyera, more powerful models are required to solve the nonlinear problems with greater precision and less cost.The artificial neural networks (ANN) are born in this background, and by far, in spite of brimming withdisputes on the transparency and interpretability, are generally acknowledged as the most robust and flexiblemodel especially for predicting work. In the ANN applications on EWS model construction, Nag and Mitra(1999), Oh et al. (2006) and Fioramanti (2008) have successfully predicted the currency, stock and debt crisesby hiring the feed-forward multi-layer perceptron. Figure 3 shows such architecture of a three-layer neuralnetworks embedded on 4-cell input later, 6-cell hidden layer and 1-cell output layer. In practice, the count ofneurons in the input layer is required to be same with the dimension of input predictors and the cell numberdetermination for hidden layer will be in trials that start from 2 and increase at a rate of 2 power . As increasingthe structural complexity will influence the networks predicting performance, especially highly winded networkswill bring over-parameterization and then make the model less generalized beyond the trained samples, sometechniques such as drop out and early stopping thus will be hired to alleviate the over-fitting problem.The neurons in each layer provide driving force to aggregate information by hiring activation functions. Aplenty of activation functions, such as sigmoid , ReLU and tanh , are available to process various nonlinearrelationships according to the property of learning target. In the study, we hire
ReLU and sigmoid activationfunctions for the hidden and the output layers respectively. They have formulations as follows.ReLU: f ( x ) = (cid:40) x, if x > , , otherwise. (17)sigmoid: f ( x ) = 11 + e − x . (18) The experimental options for hidden layer structure are 2,4,8,16,32. igure 3: The structure of a sample three-layer artificial neural networks. Green circles are cells of activation functions to processinformation before passing through the corresponding layer. The arrows represent the information flow direction from input tooutput, where red and blue label the positive and negative edge proportional to assigned weights. Before the output being processed, the weight parameters vector will be applied for each layer neurons, thusthe aggregated information can be normally connected. Denote w and w to be the weight parameters forbridging between (1) input layer and hidden layer and (2) hidden layer and output layer. Thus, the predictedresult for a three-layer ANN with n input variables, m -cell hidden layer and single cell output layer, can bewritten as follows, ˆ y t +1 = f ( m (cid:88) j =0 w j · f ( n (cid:88) i =0 w j,i · x i,t )) , (19)where x i,t is the value of variable i at time t , w j,i is the applied weight to the i th input neuron for producingthe input for j th hidden neuron and w j is the applied weight to j th hidden neuron output for the final singularprediction. For more than three layers model, the process can be recursively implemented by assigning variousdimensional weight parameters. The parameters will then be optimized by minimizing the L penalized objectivefunction in 100 epoch iterations. Random Forest and Gradient Boosting Tree.
Both random forest and gradient boosting tree aretree-based model on the ensemble learning base. The core idea for decision tree is to continuously partitiondata into homogeneous clusters by refining the selection rules as either building or pruning tree branches to getthe optimal tree structure. The tree-based model can naturally visualize the catergorizing rules and extract thevariable importance, the model interpretability is thus more remarkable than other machine learning techniques.Koyuncugil and Ozgulbas (2012) and Tanaka et al. (2016) use the tree-based model construct EWS for predictingrisk pressure for small enterprises and nationwide bank failures, which alters the practitioners’ perspective innonparametric models’ predicting power. We thus put two advanced tree-based models in the stylish ensemblelearning technique, random forest and gradient boosting tree, into model contrasts.
Split1
Model6 r u l e - b Model1, Split2 Model3, Split3 Model5 r u l e - b Model4 r u l e - a r u l e - b Model2 r u l e - a r u l e - a Figure 4: An example of tree model structure with three clustering rules, three splits and six regression models. Model 4, forinstance, will be implemented by all split predictors from 1 to 3 and rule 1-a, 2-b and 3-a filtered data points.
Random forest solves the decision tree’s weakness in generalization by growing multiple trees with boost-rapping aggregation. The process is implemented as follows.1. Boostrap a sample from original data and build a tree on the boostrapped sample.11. On each split of the trained tree, randomly select k features from original n predictors, where k ≤ n , thendetermine the best one among k features and partition data.2. Repeated step 1 and 2 M times, thus M different decision trees are built with corresponding randomlycombined k features and partitioned data.3. The best tree model will be determined by monitoring the error value that continuously decrease to moststable level.4. Keep the best performed model and extract the variable importance.Hence, from the implementation process for random forests, tuning parameters of k and M are inevitable todesignated. The default value for k is equal to n , one third of predictors count. While, in the study, we alter torun a loop for k taking from 1 to ( n −
1) and search for the most efficient value that minimizes the error rate .For determination of M , the iteration will first run 200 times til stabilize the error value in a low level band.The value for M , according to our experiments, is around 50 − .Gradient boosting machines make the tree-based model algorithm more adaptive. It shares the similarity ofrandom forest that the final prediction is produced on an ensemble of tree models, but its constructing way issubstantially different. Trees in random forests are built independently and each one will reach the maximumdepth, while in gradient boosting, the trees are dependent on previous fitted trees by allowing the minimumdepth. The computation steps are listed as follows.1. Initialize D and M to be the tree depth and number of iterations. Compute the average of response ¯ y asthe initial predicted value.2. Start from the first iteration 1, calculate the residual, the difference between predicted value and observedvalue, and fit a D depth tree by setting the residuals as response.3. Produce new predictions by using the fitted tree.4, The predicted value will thus be updated by recursively implementing the step 2 and 3 and adding up theprevious predicted value from past iterations.Similarly, D and M are the tuning parameters for the gradient boosting machine. In the study, we acrossvalidate D = { , , ..., } and M = { , , , ..., } , find the combination of D = 3 and M = 100 performsbest by maximizing the AUC value for binary classification . The time cost of implementing the gradientboosting machine is more pricey than random forest since the random forest constructs independent trees inparallel, the gradient boosting, though restricts the tree grown depth, aggregates previous results in an adaptiverecurring process. Attention based Long-short term memory networks.
The deeper variant of neural networks, themulti-layer perceptron models that inherently suit the time dependency, such as recurrent neural networks(RNN) and long-short term memory networks (LSTM), have been generally applied in financial predictionstudies (Fischer and Krauss, 2018; Liu, 2019; Cao et al., 2019) and present more promising forecasting powerthan plain neural networks. As Figure 5 shows, the input at time t will access the LSTM perceptron and thenpass through three ‘gates’ and a series of processing calculations to purify and aggregate information, and infinal, carry the activation function a t and peehole function C t to next cell and produce (intermediate outputfor) predicted results. Specific formulations for the LSTM cell can be written as follows. Γ f = σ ( x t U f + a t − W f ) , (20) Γ u = σ ( x t U u + a t − W u ) , (21) Γ o = σ ( x t U o + a t − W o ) , (22)˜ C t = tanh ( x t U g + a t − W g ) , (23)where σ (cid:48) s refer to activation function for each gate, x t is the input at time t , U (cid:48) s and W (cid:48) s are assigned weightparameters to connect two neighbour cells by passing processed information from past to future. The R package ‘randomForest’ implements the random forest model. The value of M is fluctuating for different data frequency. R package of ‘xgboost’ helps to fit the gradient boosting model. igure 5: The inner structure of LSTM cell. Γ f , Γ u , Γ o are sigmoid functions of the forget gate, the update gate and the outputgate that determine the information to be discarded, added and reproduced. ˜ C t is the new candidate output created by the tanh layer, which is limited in the range [ − , a t and C t are recurrently employed activation function and peehole function that carryhistoric information flow to the future memory block. The initial values of C and a are both zero. The LSTM based EWS has been proven more effective in the comparison to other two machine learningpredictive models, back-propagation neural networks (BPNN) and support vector machine (SVM), for predictingstock crashes (Wang et al., 2020a). The model is then made more comparable in terms of extracting variableimportance by stacking a upper attention layer on the LSTM layer (Wang et al., 2020b), as Figure 6 shows,before entering into LSTM cells, attention mechanism will filter out high-value information among a largeamount pieces of inputs. It revolutionizes the weakness of traditional way that assigns same weight vector toeach input, by varying the weight according to inputs’ value. Thus, a sequence of { h tt = { ,...,T } } will be madefrom a network of T LSTM memory cells that process the generated output { d tt = { ,...,T } } from attention layer,and the final prediction ˆ y T +1 will be produced by a sigmoid function to squash the value into [0,1]. The processthen will be recursively carried out on sequential sample pieces from t = { , ..., T + 1 } onward till the end at T . Three types of measurements will be adopted to examine the EWS effectiveness in terms of classifiers,predicted results and practical usefulness.
For the crisis classifier, except matching to the chronology critical events, we take an objective way of firstcalculating the misspecification rate for identified crises on the out-of-sample size truncated full samples andthe out-of-samples for each classifier, and recognizing the best performed one with the least misspecificationrate. The performance is then further validated by statistically boostrapping the 1000 sample pieces from fullobservations and take the average misspecifications.Table 2 lists the classifiers that will be put in contrast, thus a justification approach will be proposed toinvestigate the classifier identifying precision as compare with ‘true’ crisis observations. This judgement isyet objectively committed because the exact timing of ‘true’ crisis is ambiguously personalized correspondingto individuals’ cognition level on crises. Most studies alter to match the either critical events or significantsigns (Oh et al., 2006; Abiad, 2007; Sevim et al., 2014; Eijffinger and Karatas, 2019) that once appeared innotorious financial crisis periods to the identified results, but this judgement somewhat lacks of persuasion. Thestudy will though, in the intuitive judgement way, collect the chronologically published evidence to clarify theclassifier’s identifying performance, a more statistical-orient evaluating method to compare the identified crisesdifference between for full samples and for test set, as following itemized procedure described, will be proposedand implemented to avoid the subjectivity.1. Classifiers will first identify crisis observations for full samples (with size of N f ) and test set (with size of N t ) respectively, then identified crises on full sample is the vector of C f = { C , C , ..., C N f } and that ontest set is C t = { C , C , ..., C N t } ; 13 igure 6: The attention based LSTM networks structure. T is the preset time step size. Vectors of observed variables [ x t , ..., x tN ]at time t for t = { , ..., T } will be processed by activation function of tanh and probability transformation function of softmax given uniformly distributed weight vector W and a constant vector b . Then, attention filtered information will be passed to theLSTM layer for further processing til final predicted results ˆ y T +1 is generated. The dotted arrows that direct { h t,t = { ,...,T − } } means the intermediate output before T will not be memorized by LSTM cell and further be participated into the final prediction.
2. Full samples will be truncated as the same time horizon of test set and then the identified crises ontruncated full samples will be denoted as the vector of C f truc = { C N f − N t +1 , ..., C N f } ;3. Misspecification rate on the test set will be calculated asmisspefication rate = (cid:80) N t i =1 ( C f truc (cid:54) = C t ) N t , (24)To avoid the opportunist result, boostrapping will be further required to validate the classifier averageperformance, and the most preferred classifier will give the lowest average misspecification rate on boostrappedsamples. The implementing procedure is to repeat the above step 1-2 on the randomly selected piece of sampleswith the size of N t,j for B times . Then, from j = 1 to j = B , the average misspecification rate be calculatedas avg. misspecification rate = 1 B B (cid:88) j =1 (cid:34) (cid:80) N t,j i =1 ( C f truc ,j (cid:54) = C t,j ) N t,j (cid:35) (25) To examine the predicting robustness, as previous EWS studies adopt, two types of statistical measurementswill be taken (1) the goodness-of-fit, such as the ratio of correctly called crisis observations and crisis onsets, andfalse alarms (Berg and Pattillo, 1999b; Bussiere and Fratzscher, 2006; Davis and Karim, 2008; Dawood et al.,2017) on out-of-samples, and (2) credit-score calibrations, such as quadratic probability score (QPS), Youdenindex J (Candelon et al., 2012) and SAR (Caruana and Niculescu-Mizil, 2004). B is usually great larger than the sample size. The composite score of averaging the accuracy, AUC and 1-RMSE.
QP S = 1 T T (cid:88) t =1 y t − y t ) (26)Youden J : J = sensitivity + specificity − − RMSE)) (28)
To invigilate the predicted signals usefulness in practice, back testing and reality check will be hired inassigning varied portfolio weights according to the investors’ risk aversion in turmoil periods. The risk aversionlevel is proven dynamic as the financial situation shifts from tranquility to turmoil, specifically, both macro-and micro-level shocks increase the investors risk aversion level (Sakha, 2019), and then the asset allocation willbe necessarily re-adjusted to improve the portfolio returns (Hasler et al., 2019) and lower the amplifying degreefrom institutional investors’ negative behaviour to exacerbate subsequent crashes (Fan and Fu, 2020).The implementing back test process is on the basis of constructing a moving forward the dynamics for assetallocation by referring to the warning signals. Similarly to previous studies for portfolio construction (Rapachet al., 2009; Dai et al., 2020), in the study, for each asset of { r i,i =1 ,...,S } , at time t , the portfolio weight will begiven as w i,t = 1 γ + ˆ y i,t +1 ( η i,t σ i,t ) , (29)where η i,t is the return rate for asset r i at time t , σ i,t is the realized volatility with one-year rolling windowfor asset r i at time t . γ denotes the initial risk aversion level for investors, which will be varied from 1 to 3to represent the innate risk preference tastes from low to high in the real market. ˆ y i,t +1 is the produced crisiswarning signal from each EWS model for asset r i . Here, the short sales is restrained no more than 50% and thelong position is allowed no more than 150%, the value of w i,t will be hence limited into ( − . , .
5) (Campbelland Thompson, 2007; Dai et al., 2020).Sharpe ratios and the average certainty equivalent return (CER) will be then calculated as follows,Sharpe ratio = R p σ p (30)CER = R p − γσ p (31)where R p and σ p denote the mean and standard deviation of portfolio returns, R p = (cid:80) Si =1 w i,t η i,t .The reality check will be implemented by revisiting the Eq. 32, portfolios’ realized variance (Wang et al.,2020a) between the EWS involved and non-EWS benchmarks, and make judgement on whether the null hy-pothesis of EWS not improving the return variance level, i.e. H : E ( f ) ≥
0, will be rejected after stationaryboostrapping 1000 times for p-value calculation. f t = V EW S,t − V Bench,t (32)
3. Experimental study on currency and stock markets in China
As the world’s second largest economy, financial markets in China have been continuously improving in ablossom development and rapidly expanding international economic interactions. It is, however, the high-speed“Oreint Express” opts to an unpredictably changing economic situation and follows the endeavour to maintainthe market stability, especially for two principal markets of currency and stocks, in the financial crisis triggeredturbulence. For the currency market, after the “8.11” Exchange Rate Reform in 2005, the Central Bank hasbeen reduced their intervention in manipulating the exchange-rate to lowest portion. According to the releaseddata released from the Bank for International Settlements (BIS), the nominal effective exchange rate of theChinese yuan (CNY) appreciated 38% from the beginning of 2005 to June 2019, and the real effective exchangerate appreciated 47%, which not only leads China to be one of the largest currencies in the globe, but gains theexposure risk to financial crises as well. For the Chinese stock market, it has experienced tremendous ups anddowns in financial crises and also has been playing as the barometer of economic situation for more than threedecades, from the original grassroots era (1990-1995), the golden age (1995-2000) to the era of returning to reason(2000-2005) and prosperity (2005-2010), and to the most recent fanaticism caused stock crash (2015-2016). The15ossibility of constructing an effective predictive system to monitor two primary investment markets turbulencewill gain the economy reliance to crash risks and guide the policymakers and investors to avoid devastatinglosses in the withering attacks.To fulfill the aim of comparing EWS model predicting effectiveness on market specific crises and unravelmystery of whether any forecasting system will work on Chinese markets, which were once thought to be lesstransparent and highly government-manipulated, we thus experiment on both currency and stocks markets ofChina.
Two prerequisites for sourcing data are (1) substantial variables are reserved in the a credible database,and (2) the variables have been studied and proven closely linked to predicting financial crises. Referring toKaminsky et al. (1998) study who have listed the most comprehensive table for crisis leading factors from variouseconomic sectors, we similarly source 36 variables, including 8 daily, 17 monthly and 11 annually distributedfactors corresponding to the currency and stock turbulence variations. For instance, in the national economysector, external factors such as reserves and the real exchange rate, and financial factors such as domesticcredit to GDP and interest rate, have already been proven capable of signalling the economic vulnerability incurrency crashes for China (Peng and Bajona, 2008). Most variables are obtainable from WIND database,except discount rate and crude oil price from St. Louis Fed and gold price from World Gold Council (WGC).Time horizon covers from December 1 st of 1995 to December 1 st In this section, we first calculate the misspecification rate for each crisis classifier to compare the identifyingrobustness on different size samples, and then, similarly to previous studies, put the critical crisis events inchronological order to contrast the identified periods. The classifiers all listed in 2 will be implemented. Inpractice, the value for scaling coefficients of λ fpi and λ cmx are experimented as 1 . , respectively.The crisis classifier robustness will be measured in evaluating the stability of classified results as vary thecrisis turmoil intensities for different pieces of observations. We implement all classifiers on full samples andtest set to clarify their each performance by following the described procedure in the Section 2.3.1. The testset for both non-boostrapping and boostrapping experiments is taken as one thirds of full samples. Table 6shows that, among the classifiers, the (average) misspecification rates given by the SWARCH opt classifier aresmallest, 1 .
81% and 13% for currency and 2 .
09% and 9 .
56% for stocks, on daily and monthly identificationsrespectively. The classifier based on the SWARCH with the arbitrary cutoff, however, gives the most miserablemisspecifation rates of 4 .
63% and 14 .
1% for currency on daily and monthly basis, and 4 .
51% for stock dailybasis. It gives 10 .
4% for identifying monthly stocks, which is not worse than the CMAX brought value of11 .
6% but not enough to reverse its feebleness on crisis identification. In short, the crisis classifier built on theSWARCH with two-peak dynamically threshold is statistically proven to be the most robust one. In furthercomparisons, the SWARCH with arbitrary cutoff of 0.5 classifier will be ruled out to condense the distinctionbetween the classic quantization index and the SWARCH methodologies.The ‘observable’ financial crisis periods and their relevant starting sign evidences during the most recent 24years from 1996 to 2019 will be chronologically displayed and visualized, as Table 7, 8 and Figure 7 in AppendixII show, to investigate the credibility of crisis classifier’s identifications in an intuitive way.The highlighting session, such as 1997 Asian financial crisis, 2007-08 Global financial crisis, 2010-11 SovereignDebt crisis and 2018 Sino-US trading war are cross-national financial crises for both markets, otherwise are WIND is a popular qualified financial database in mainland China. It contains both micro- and macro- economic variable datafor researchers and practitioners. The only shortage is that the access is limited to commercial usage. Gradient searching is implemented in the set of { , . , , . , } and the best performed value is taken with the minimalmisspecification rate. The count of regimes K is determined by calculating the RCM. able 4: Summary of factor variables. Sector Label Variable Frequency SourceStock market ssec Shanghai composite index daily WINDssec r return rate of Shanghai compos-ite index dailysez Shenzhen composite index dailysez r return rate of Shenzhen compos-ite indexCurrency market frx USD/CNY exchange price daily WINDfrx r return rate of USD/CNY ex-change price dailyInterest rate dis r discount rate monthly St. Louis Fedint r demand deposit interest rate monthly WINDNational economy bal g balance of international pay-ments (% in GDP) annually WINDcci consumer confidence index monthlycpi consumer price index (year-on-year basis) monthlycomd g commodity trade (% in GDP) annuallydeb g total debts (% in GDP) annuallydom c domestic credit monthlydom g banking departments offered do-mestic credit (% in GDP) annuallyfix a completed investment in fixedasset(cumulative year-on-yearbasis) monthlyfrx res official foreign exchange reserve monthlygdp p per capital GDP annuallygdp p2 per capital GDP (year-on-yearbasis) annuallygdp c GDP growth contribution rate(to consumption) annuallyim ex total import-exportvolume(year-on-year basis) monthlyind g industrial added value (% inGDP) annuallyind p production and sales ratio of in-dustrial products monthyind v industrial added value (year-on-year basis) monthlyinf r inflation rate annuallymac c macro-economic climate index monthlym2 g board money supply (% in GDP) annuallyppi producer price index (year-on-year basis) monthlyreal c real-estate climate index monthlyrpi retail price index (year-on-yearbasis) monthlyrrr reserve requirement ratio monthlyshibor Shanghai interbank offered rate(weighted averge) monthlytax r tax revenue monthlyGlobal economy gold global gold price (US dollarwise) daily World Gold Counciloil crude oil price (West Texas In-termediate) daily St. Louis Fedvix S&P500 volatility index daily WIND able 5: Statistic descriptions Variable Mean Standard Dev. Skewness J.B. Statistic Countssec 1793.40 1039.33 1.08 1632.6 5686ssec r 0.09 2.65 12.15 48754295 5685sez 5793.46 4209.13 0.96 829.22 5686sez r 0.07 2.21 0.96 45313 5685frx 7.39 0.85 -0.12 706.4 5686frx r 0.00 0.11 0.43 529747 5685dis r 3.80 1.84 2.40 466.99 257int r 0.78 0.59 2.09 427.95 257bal g 4.83 3.80 0.25 0.94875 26cci 109.42 6.22 0.50 10.857 257cpi 2.26 2.53 0.81 32.581 257comd g 42.75 10.56 0.67 2.803 26deb g 27.19 12.32 0.33 1.2994 26dom c 599448 606773 1.18 60.85 257dom g 148.22 39.80 0.53 1.9997 26fix a 19.59 8.87 0.19 2.1097 257frx res 16761 13999 0.19 30.582 257gdp p 28953 22391 0.57 2.7291 26gdp p2 8.22 1.99 0.82 3.4763 26gdp c 56.57 11.92 0.65 2.2989 26im ex 13.66 15.97 0.02 2.6891 257ind g 44.70 2.52 -0.77 3.6808 26ind p 97.73 1.29 0.32 210 257ind v 11.46 4.27 0.21 10.587 257inf r 2.82 3.60 2.22 75.228 26mac c 96.44 3.31 -0.03 8.5258 257m2 g 162.25 32.64 -0.18 1.2309 26ppi 0.95 4.09 0.02 7.3328 257real c 101.28 3.63 -0.58 15.889 257rpi 1.23 2.61 0.53 11.965 257rrr 12.88 5.20 0.01 22.948 257shibor 3.39 2.73 2.32 434.42 257tax r 5061.64 4341.54 0.82 30.973 257gold 829.69 481.28 0.24 549.98 5686oil 54.46 28.87 0.46 329.34 5686vix 19.90 8.14 2.08 1766 5686 able 6: Compare classifiers’ robustness: count of misspecified crisis observations. panel (a) : currency FPI SWARCH SWARCH opt days months days months days monthsCount of crises on full samples 25.0 48.0 1529 83 1517 83Count of crises on truncated full set 22.0 24.0 1092 52 1086 52Count of crises on test set 21.0 12.0 1034 55 1075 51Count of misspecified obs. 20.0 12.0 75.0 13.0 15.0 9.0% of misspecified obs. 1.05 13.9 3.96 15.1 0.791 10.5Avg. count of misspecification 25.9 12.0 87.7 12.3 34.4 11.3Avg. % of misspecification 1.37 13.8 4.63 14.1 1.81 13.0panel (b) : stock CMAX SWARCH SWARCH opt days months days months days monthsCount of crises on full samples 509 38.0 2097 148 2135 137Count of crises on truncated full set 172 15.0 641 25.0 653 21.0Count of crises on test set 202 21.0 646 37.0 640 27.0Count of misspecified obs. 30.0 6.00 25.0 12.0 25.0 6.00% of misspecified obs. 1.60 6.89 1.32 13.8 1.32 6.89Avg. count of misspecification 53.5 10.1 85.5 9.07 39.7 8.32Avg. % of misspecification 2.86 11.6 4.51 10.4 2.09 9.56 national stylized critical facts, such as 2013 ‘Cash Crunch’, 2015 Chinese stock market crash and macroeconomiccontrol policy for specific market. In end of 90’s Asian crisis, the currency market experienced seemly vibrationsin the ‘managed floating’ scheme, unlike the violent up and down stock index which heavily oscillated till 2000. In2001, to deepen the enterprise reform, government decided to reduce the state-owned shares from stocks, whichdirectly led an almost 40% decline of SSEC in a half year. During 2004-2005, both markets were announcedto be reformed, which made 2.1% overnight depreciation for RMB against U.S. dollar and 11% annual fall forA-shares price in both SSEC and SZSE. In the periods of notorious 2008-09 financial crisis and its follow-up2010-11 Sovereign debt crisis, Chinese yuan devalued 15% before pegging to the U.S. dollar and the bear marketfor stocks lasted for more than three years till the second half of 2012. In late May of 2013, the panic inducedby inter-bank market capital shortage, alternatively called ‘Cash Crunch’, spread to the stock market, whichled SSEC a 16% reduce in June. In 2014 Feb.,China took actions to guide the Chinese yuan weaker and swiftlyturned to expand the volatility range into ±
2% in March, which brought in Chinese yuan against U.S dollardrastic vibration in a few months. 2015 is the nightmare for Chinese stock investors. On June of 2015, aftera chain of reactions between off-site allocation clean-up, on-site financing and deleveraging of graded funds,Chinese stock market was led to a severe crash that most stocks declined more than 50% in twin-weeks, whichtouched off the fusing mechanism by imposing dual-thresholds of 5% and 7% on the index fusing benchmark.Even worse, a resonant effect was formed between the currency and stocks as soon as the ‘one basket currencies’policy was published, which devaluate yuan against U.S. dollar by 5 . able 7: Identified crisis episodes for currency market. critical event evident sign FPI SWARCH opt −− . ± . −− ± .
0% since 2014March. 2014.06-12;2015.03-07 2014.03,04,09,12;2015.03,042015 ‘One basket currencies’scheme and Chinese stockcrash Starting from 2015summer, the ‘stock-exchange resonance’ ledyuan against U.S. dollardropped 5 . −− able 8: Identified crisis episodes for stock market. critical event evident sign CMAX SWARCH opt −− −− −− −− −− The predicted results will be displayed in two aspects of the hit-ratio calculations, including the correctpredictions, correctly called onsets, false alarms and predicted days in advance, and the statistical calibrationmetrics of QPS, Youden J and SAR. Table 9 and 10 give the calculated values on out-of-samples in terms of daily(short-term) and monthly (long-term) data frames for currency and stock markets respectively, where the bestperformed metrics are bold-type in each row to present the corresponding combined EWS model performance.Comparing the results in sub-panels of (a)/(b)-1 and (a)/(b)-2, we verify that SWARCH classifier can trulyboost the EWS performance in terms of either higher predicting precision or lower false calling alarms especiallyas combine econometric models of logistic regressions. For instance, the FPI combined LR gives 61 .
5% correctlycalled crisis observations and 28 .
1% false alarm rate while the SWARCH hybrid LR improves the values by20 .
8% (to be 82 .
3% correctly predicted crises) and 28 .
1% (to be 0 .
00% false alarms) for currency market short-term prediction. SWARCH shares a similar boosting on KLR, except for stock long-term prediction, neither thehit ratios for predicted crisis observations and predicted crisis onsets nor the statistical metrics for Youden J and SAR get significant improvements. Among the machine learning techniques, the classification tree modelsof RF and XGBoost can benefit from SWARCH classifier by diminishing the false alarms. For example, for theshort-term prediction on currency market, the percentage of false alarms produced by FPI combined RF modelis 23 .
1% while being decreased to be 0 .
00% as substituting the SWARCH classifier. Besides, the SWARCHcombined EWS model will provide longer early warning periods especially for long-term predictions. Thetypical evidence can be found as compare the row of hit(4) between (b)-1 and (b)-2 in Table 9, that the calledadvanced days for crisis onsets have been prolonged for 1-2 months, which implies ample reaction time will besuggested to regulators or decision makers to respond the market vulnerability.In addition, the EWS model based on machine learning predictive techniques outperforms that based ontraditional econometric models with better goodness-of-fit and statistical scores especially as the SWARCHclassifier joins. The average hit ratio of correct predicted crises extracted from NN, RF, XGBoost and AttnLSTMbased EWS is greater than 90% for both markets predictions (except the short-term prediction for stock withCMAX classifier), which wins the LR and KLR that model hardly get more than 90% correct predictionswith a commanding lead. Furthermore, most zeros of QPS and ones of Youden J metric values are givenby SWARCH combined machine learning models, which also strongly validates the predicting robustness ofthese hybrid state-of-art brain-like learning models. In fact, it is quite differential to specify machine learningmodels forecasting power, for instance, even though classification tree models of RF and XGBoost bring in 100%predicting precision on crisis observations and 0 .
00% false alarms (as refer to the hit (1) and hit (3) in (a)-2and (b)-2 sub-panels for both markets), the neural networks of NN and AttnLSTM generally perform betteron predicting crisis onsets and advanced days (as refer to hit (2) and hit (4) in (a)-2 and (b)-1 of Table 9 and(a)/(b)-2 of Table 10).In contrast to previous study on comparing econometric models constructed and machine learning basedwarning system for predicting banking crisis that claims conventional models already fairly efficient to useavailable information (Beutel et al., 2019), we conclude a different pattern in line with the measured resultsthat the machine learning based predictive models, especially the deep learning based EWS, will not lose eithercredibility or robustness on out-of-sample predictions given sufficient endogenous and exogenous features dataand SWARCH model inferences.To concentrate the model comparisons in a compact way, we further clarify a series of refining conditions into a unified system. As Table 11 shows, the selection standards are listed at the left side and models that canpass through each selection condition will then be screened till the the final row, the most frequently screenedmodel that is picked as the best EWS for predicting corresponding market and required term displays. Accordingto final model options, SWARCH crisis classifier is indisputably preferred to both markets for both short- andlong- term prediction. The market however shows idiosyncrasy in predictive model selection. Particularly, thestock market is solely partial to the AttnLSTM, while the currency market seems to prefer both of NN andAttnLSTM for short-term prediction and extra includes the RF for long-term prediction. To avoid ambiguousmodel determinations, further comparisons for currency market are required. Back to Table 9, AttnLSTM andRF produced more bold-labelled results for short-term panel (refer to (a)-2) and long-term panel (refer to (b)-2)respectively. Thus in brief, the unified comparison suggests the SWARCH-AttnLSTM as the best option for The refining conditions are statistical metrics with appropriate threshold level to rule out unsatisfied models. The thresholdvalue can be country or market personalized in practice. able 9: Compare EWS models predictive power: hit-ratios and score metrics for currency. panel (a): short-term LR KLR NN RF XGBoost AttnLSTM(a)-1: FPIhit(1) a b hit(3) c d ∗ ∗ ∗∗ ∗ Youden J
100 100 100 hit(2) 45.5 55.3 84.5 0.00 54.5 hit(3) 0.00 32.9 ∗∗ hit(4) 3.07 2.39 ∗ ∗∗ ∗∗ ∗ Youden J panel (b): long-term LR KLR NN RF XGBoost AttnLSTM(b)-1: FPIhit(1) 66.7 70.8 91.7 -0.096 J
100 100 100 hit(4) 2.46 2.5 2.8 ∗ ∗∗ ∗∗ ∗ Youden J a % of correctly called crisis observations. b % of correctly called onsets. c % of false alarms. d count of alarming advanced days. ∗ , ∗∗ refer to with 5% and 1% significance level respectively. able 10: Compare EWS models predictive power: hit-ratios and score metrics for stock. panel (a): short-term LR KLR NN RF XGBoost AttnLSTM(a)-1: CMAXhit(1) 49.1 47.2 79.2 63.2 56.6 hit(2) hit(3) 43.1 46.4 36.1 ∗ -0.10 0.00 ∗ -0.07 -0.07 0.00 ∗ Youden J SAR 0.643 0.656 0.581 0.102
100 100 100 hit(2) 63.2 61.9 47.4 47.4 47.4 hit(3) 38.7 50.4 ∗ hit(4) 2.74 2.47 ∗ ∗∗ ∗∗ ∗ Youden J panel (b): long-term LR KLR NN RF XGBoost AttnLSTM(b)-1: CMAXhit(1) 59.3 76.3 hit(2) 0.00 50.0 hit(3) 40.6 48.2 11.1 12.0 QPS 0.813 0.180 J (b)-2: SWARCHhit(1) 84.2 73.0
100 100 100 100 hit(2) 0.00 50.0 hit(3) 39.3 26.2 20.0
QPS 0.277 -0.127 0.185 ∗∗ ∗∗ ∗ Youden J a b l e : M o d e l s e l ec t i o n f o r c u rr e n c y a nd s t o c k m a r k e t s . m a r k e t c u rr e n c y s t o c k s c l a ss i fi e r F P I S W A R C H C M AX S W A R C H p a n e l ( a ) : s h o r t - t e r m h i t( ) > NN , R F , X G B oo s t , A tt n L S T M NN , X G B oo s t , A tt n L S T M – L R , NN , R F , X G B oo s t , A tt n L S T M h i t( ) > NN , A tt n L S T M NN , A tt n L S T M – A tt n L S T M h i t( ) < L R , NN , R F , X G B oo s t , A tt n L S T M R F , X G B oo s t NN , R F , X G B oo s t , A tt n L S T M h i t( ) > d a y s X G B oo s t L R , NN , X G B oo s t – NN , R F , X G B oo s t | Q P S | < . NN , R F , X G B oo s t , A tt n L S T M NN , R F , X G B oo s t , A tt n L S T M L R , NN , A tt n L S T M NN , R F , X G B oo s t , A tt n L S T M Y o ud e n J > . R F , X G B oo s t NN , R F , X G B oo s t , A tt n L S T M – NN , R F , X G B oo s t , A tt n L S T M S A R > . R F L R , R F , A tt n L S T M – A tt n L S T M b e s t m o d e l S W A R C H - NN / A tt n L S T M S W A R C H - A tt n L S T M p a n e l ( b ) :l o n g - t e r m h i t( ) > NN , R F , A tt n L S T M K L R , NN , R F , X G B oo s t , A tt n L S T M NN , R F , A tt n L S T M NN , R F , X G B oo s t , A tt n L S T M h i t( ) > K L R L R , K L R , NN , R F , X G B oo s t , A tt n L S T M NN , A tt n L S T M NN , A tt n L S T M h i t( ) < X G B oo s t , A tt n L S T M NN , R F , X G B oo s t , A tt n L S T M X G B oo s t R F , X G B oo s t h i t( ) > m o n t h K L R L R , K L R , NN , R F , X G B oo s t , A tt n L S T M – K L R , A tt n L S T M | Q P S | < . NN , R F , X G B oo s t , A tt n L S T M – R F , X G B oo s t , A tt n L S T M Y o ud e n J > . NN , R F , X G B oo s t , A tt n L S T M NN , A tt n L S T M R F , X G B oo s t , A tt n L S T M S A R > . NN , R F , A tt n L S T M NN , A tt n L S T M NN , R F , A tt n L S T M b e s t m o d e l S W A R C H - NN / R F / A tt n L S T M S W A R C H - A tt n L S T M The predictive models in the financial applications that are blamed for its lack of practical verification bearthe questioning on whether the predictability is equivalent to the effectiveness in real world. Thus the dynamicalportfolio allocation will be applied according to investors’ risk aversion variation given properly predicted thecrisis episodes, thereby to validate whether the prominent crisis forecasting system will bring attractive returnsin practice.
Table 12: Back-test results of asset allocation on out-of-samples. risk aversion level low: γ = 1 medium: γ = 2 high: γ = 3panel(a): daily Sharpe ratio CER Sharpe ratio CER Sharpe ratio CERbenchmark buy-and-hold 0.236 7.74 0.241 -2.66 0.244 -6.12TQI 0.307 8.42 0.306 0.204 0.291 -3.67SWARCH 0.454 10.2 0.442 2.25 0.390 -2.82TQI - -LR 0.344 8.04 0.302 1.33 0.288 -2.36-KLR 0.234 7.76 0.238 -0.943 0.243 -3.37-NN 0.362 7.83 0.312 1.65 0.295 -2.24-RF 0.351 7.84 0.305 1.40 0.289 -2.31-XGBoost 0.336 7.85 0.340 0.893 0.344 -2.34-AttnLSTM 0.368 8.67 0.372 1.43 0.391 -2.28SWARCH - -LR 0.498 10.8 0.441 2.92 0.391 0.015-KLR 0.504 9.31 0.440 2.86 0.389 0.010-NN 0.517 11.8 0.443 2.89 0.391 0.020-RF 0.508 11.0 0.442 2.89 0.390 0.004-XGBoost 0.508 10.5 0.442 2.89 0.391 0.008-AttnLSTM 0.518 11.5 0.461 3.22 0.407 0.024panel(b): monthly Sharpe ratio CER Sharpe ratio CER Sharpe ratio CERbenchmark buy-and-hold 0.409 20.3 0.448 -14.1 0.478 -26.3TQI 0.448 22.2 0.469 -15.6 0.481 -27.6SWARCH 0.497 22.4 0.502 -10.8 0.509 -20.5TQI - -LR 0.517 24.5 0.495 -3.65 0.496 -14.3-KLR 0.505 23.8 0.487 -2.27 0.503 -13.6-NN 0.534 27.2 0.455 -2.92 0.462 -15.8-RF 0.492 22.4 0.499 -0.07 0.508 -11.3-XGBoost 0.493 22.5 0.499 -0.07 0.509 -11.1-AttnLSTM 0.541 26.8 0.519 1.57 0.526 -10.3SWARCH - -LR 0.503 22.6 0.505 0.350 0.506 -11.4-KLR 0.519 25.8 0.492 -0.741 0.497 -15.8-NN 0.516 23.9 0.509 0.473 0.512 -11.0-RF 0.513 23.8 0.512 0.782 0.513 -11.3-XGBoost 0.513 23.8 0.512 0.781 0.514 -11.2-AttnLSTM 0.556 29.8 0.534 2.24 0.528 -10.5 In the study, three assets of SSEC index, exchange rate against U.S. dollar and risk-free interest willbe accounted into the back test. To make a fair situation, we impose a key assumption that no informativeasymmetry exists as practitioners access the early warning model outputs and construct the portfolio based onthe produced warning signals varied risk aversion. Three benchmark portfolios will be constructed by taking‘buy-and-hold’, solely applied ‘TQI’ and solely applied ‘SWARCH’ strategies that not involve predicted results.Table 12 shows the Sharpe ratios and Certainty Equivalent Return (CER) under different constant baserisk aversion levels of low, medium and high for both daily and monthly exercising scenarios. Among threebenchmarks, the crisis classifier adopted portfolios, especially the SWARCH classifier adopted, is most preferredby either doubling (for short-term daily panel) or gaining a quarter (for long-term monthly panel) than the lowrisk aversion buy-and-holders produced Sharpe ratios. In panel (a), as compare to buy-and-hold, the TQI based The risk-free rate is adopted as the bank short-term deposit interest rate. . .
461 and 0 . . γ = 1, of 3 .
22 and 0 .
024 among all calculations, and it still winsin the long-term investment but with a weak edge.We also find the EWS may reverse investors earning profit situation according to their risk aversion level.Particularly, the high-risk seeker ( γ = 1) who previously have lower Sharpe ratios than conservative investors( γ = 3) as holding benchmark portfolios will benefit more as apply the EWS to adjust portfolio weightsespecially for short-term investment. This conclusion is consistent with Hasler et al. (2019) who claim thataccounting for timing of equity risks will advantage the investing portfolio returns by increasing the CER of 3%.Meanwhile, since the selling pressure of short-term investors is proven positively linked to market crash (Fanand Fu, 2020), the dynamically constructed portfolio according to EWS produced warning signals will faithfullysupport practical solution to adjust asset weights and to further avert dreadful panic that always manifests inuninstructed situation.To investigate whether the EWS forecasting robustness in back-testing is accidental or not, reality checkwill be implemented. The benchmarks mainly keep same settings as back-testing, but will be slightly changedin opting the EWS contrast group, that is the benchmark of TQI crisis classifier will only appoint to TQI basedEWS models group and vice versa. This setting will project the predictive models effort more in comparisons.Table 13 reasons the credibility of back-testing results given p-values below 0 .
1, which indicates the nullhypothesis that the EWS does not help to diminish the return variance can be strongly rejected. The p-valuesthat exceed 0 . .
1, mainly locate in TQI-XGBoost based EWS for daily prediction and traditionaleconometric models of LR and KLR based EWS for monthly prediction, which cautions investors against suchEWS models that may produce less reliable results to minimize the volatility triggered risks in returns. Besides,the SWARCH combined machine learning EWS models, especially combined tree models of RF, are most likelyto pass through the reality check by harvesting more zero or close to zero p-values in the comparison. Thehighly recommended model in back-testing, SWARCH-AttnLSTM, however puts a bit of damper by losingcredibility at 0 .
05 level, specifically providing 0 . .
049 and 0 . p B ’s are generally smaller than p B ’s, which implies the returnvariance harder to be kept lowering as predictive model is introduced after identified crisis being applied toameliorate the asset returns, the machine learning hybrid EWS models adopted on monthly prediction strikethe this suspicious assertion by giving smaller p B than p B , for example SWARCH-NN/RF/XG present p B zero at 0 .
1% significant level but p B greater than 0 .
01 for low and medium risk aversion investors.In general, the SWARCH combined machine learning models generally outperform among the developedhybrid EWS models, and such stylized models show comparative practical persuasion in varied investing riskpreference. Traditional econometric models, especially combined with the classic technically quantified indexcrisis classifier, seem to faintly satisfy modern requisite on not only the high predicting precision but thedemanding portability in practice. Hence, on the premise that both data quantity and quality can be guaranteed,the investors or decision makers are more likely to appeal to the stylized warning systems instructed warningsignals.
The estimation on leading factors will not only attribute the contributing degree to inform of predictingcrises, also distinguish the factors that should be regularly inspected among multi-source information as well.For each applied predictive model, the input features importance can be estimated and extracted from modelproduced results, specifically, the logistic regression bases on the parameter’s coefficient, non-parametric KLRapproach relies on the calculation for noise-to-signal ratios, neural networks have dropping one factor each timeto infer the accuracy loss as feature importance, random forest hires the metric of mean decrease accuracy27 able 13: Reality check on EWS model robustness. risk avresion level low: γ = 1 medium: γ = 2 high: γ = 3panel (a): daily p B a p B a p B p B p B p B TQI- -LR 0.039 0.054 0.016 0.084 0.021 0.083-KLR 0.031 0.110 0.029 0.091 0.021 0.086-NN 0.060 0.090 0.047 0.111 0.036 0.102-RF 0.001 0.011 0.005 0.012 0.010 0.011-XG 0.087 0.125 0.079 0.092 0.078 0.083-AttnLSTM 0.051 0.081 0.043 0.082 0.037 0.072SWARCH- -LR 0 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ -XG 0 ∗∗∗ ∗∗∗ p B a p B a p B p B p B p B TQI- -LR 0.070 0.156 0.071 0.159 0.071 0.121-KLR 0.050 0.171 0.064 0.124 0.049 0.133-NN 0.031 0.066 0.032 0.067 0.036 0.067-RF 0.018 0.014 0.016 0.015 0.008 0.013-XG 0.017 0.014 0.019 0.020 0.008 0.010-AttnLSTM 0.019 0 ∗∗∗ ∗∗∗ ∗∗∗
SWARCH- -LR 0.019 0.091 0.017 0.083 0.007 0.075-KLR 0.057 0.079 0.054 0.076 0.056 0.092-NN 0.020 0 ∗∗∗ ∗∗∗ ∗∗∗ -RF 0.020 0 ∗∗∗ ∗∗∗ ∗∗∗ -XG 0.019 0 ∗∗∗ ∗∗∗ a B is the benchmark of buy-and-hold. B is TQI for TQI based EWS and SWARCH for SWARCH based EWS. ∗∗∗ denote at 0 .
1% significance level. (MDA) , XGBoost uses the gain that represents the fractional contribution of each factor based on the totalgain of this factor’s split, and the attention based LSTM extracts the final learnt attention weights for eachfeatures.Table 14 further summarizes the model detected leading factors by collecting the estimated results on factorcontribution that are displayed in Table 15-18, where the highlighted bold numbers are recognized significantimpact on the crisis prediction. According to the Table 14, the most frequently drawn factors are frx (exchangerate), gdp p2 (per capital GDP year-on-year basis) and ind g (industrial added value as the percentage ofannual GDP), which suggests that currency exchange rate dynamics itself and macroeconomic factors relatingto the national production situation should be early cautioned for crisis prediction regardless of the predictionterm. In fact, the real exchange rate has been proven to be the most significant leading factor for predictingcurrency crisis (Kaminsky et al., 1998; Berg and Pattillo, 1999b; Babeck´y et al., 2013), and meanwhile providesthe significant evidence to be contagious to the stock market (Chatzis et al., 2018), which factor also getsaccreditation in our study. It is noted that, the reverse contagion relationship from stock to currency seems tonot exist since the neither stock index dynamics nor stock return rate significantly contribute to currency crisisprediction. Different from previous argument (Kaminsky et al., 1998; Berg and Pattillo, 1999b) that claimsthe reserves and exports are crucial to indicate currency crisis, we find rare connection between such factors(frx res and im ex) and Chinese currency and stock market crisis forewarning, in contrary, the domestic economyrelated indicators (gdp p2 and ind g) are highlighted. It implies that the market turbulence is more likely tobe prepended by the forthcoming economy recession, not be fully signed by the monetary policy control andinternational trades. Furthermore, the leading factors that precede to the market crisis are essentially different, There are in fact two metrics for RF to draw the feature importance, mean decrease accuracy (MDA) and mean decreaseGini (MDG). In the study, we take MDA since its observed value variation is more distinctive than MDG provided in terms ofinformation gain.
28n some case, even market-characteristic, for instance, the inflation factors, such as discount rate and CPI, arehardly ignored in signing the long-term currency crisis but do not share any contribution to warn stocks. Thismay imply the domestic money purchasing power could drive the volatile level of foreign exchange market inthe fiscal policy channel, but seems not possibly to rock the share prices.
Table 14: Leading factors: summary of model detected leading factors for currency and stock market. currency stocksshort-term long-term short-term long-termssec (1)RF (4)NN,RF,XG,Attnssec r (2)XG,Attnsez (2)RF,XGsez rfrx (3)KLR,NN,RF (3)KLR,NN,Attn (2)NN,Attn (3)LR,KLR,Attnfrx r (4)NN,RF,XG,Anntfrx resdis r (3)NN,RF,XGint r (1)LRbal g (2)KLR,RF (2)XG,Attn (3)KLR,RF,Attncci (2)KLR, Attncpi (1)XGcomd g (1)LR (2)KLR,Attndeb g (1)LR (1)LR (2)LR,KLRdom c (2)RF,XGdom g (1)LR (3)KLR,NN,Attnfix agdp p (1)KLR (1)KLRgdp p2 (2)LR,NN (2)RF,XG (2)KLR,Attn (1)RFgdp c (1)NNim exind g (2)LR,NN (2)NN,Attn (3)LR,NN,Attn (1)LRind p (3)KLR,XG,Attnind vinf r (1)KLR (1)LR (4)NN,RF,XG,Attnmac c (3)LR,KLR,RFm2 g (1)KLRppi (2)RF,XG (3)NN,XG,Attnreal c (1)LR (1)XGrpi (2)LR,XGrrr (1)KLRshibortax rvix (2)XG,Attn (2)RF,Attngold (3)NN,RF,XGoil
The summarized table information also instructs short-term and long-term investments in inspecting theleading factors with varied perspectives. On one hand, the return rates more influence than the price/index itselfon short-term prediction, for instance, XGBoost and Attention-LSTM catch the ssec r, and neural networks,random forest, XGBoost and Attention-LSTM catch the frx r to predict stocks and currency market in short-term, but disappear to hint the long-term crisis. On the other hand, the short-term prediction requires moregovernment published composite factors from external economy sectors, such as the macroeconomic climateindicator (mac c), the real-estate climate index (real c) and PPI (ppi), and globe market dynamics index, forinstance VIX (vix), to be referred than long-term. It thus advises short-term investors to take full considerations,not merely on the price dynamics and market directly related factors, but recruit external economic information,especially the authority labeled index and globe economy dynamics, as well, to improve their risk resistancebefore the economy sloping down begins. 29 T a b l e : E s t i m a t e d c o n t r i bu t i o nd e g r ee o ff a c t o r v a r i a b l e s f o r c u rr e n c y m a r k e t : s h o r t - t e r m p r e d i c t i o n . C o e f . a L R N S R K L R I m p . e NN M D A R F I m p . X G B oo s t W g t . e A tt n L S T M ss e c . ( ) . −− c . . . ss e c r - . ( ) . −− . . . s e z - . ( ) . . . . . s e z r . ( ) . −− . . . f r x - . ( ) . . . . . f r x r . ( ) −− b . . . . f r x r e s - . ( ) . . −− d . d i s r . ( ) . . . . . i n t r . ( ) I n f b . −− . b a l g - ( ) . −− −− . cc i - . ( ) . . . . . c p i . ( ) −−−− . −− . c o m d g . ( ) . −− −− . d e b g . ( ) . −− . −− . d o m c - . ( ) . . . −− . d o m g - ( ) . −− . −− . fi x a671 . ( ) . . . . dpp - . ( ) . −− . −− . dpp . ( ) I n f . . −− . dp c - . ( ) . −− . . i m e x . ( ) −−−− . . i nd g - ( ) . . . −− . i ndp - . ( ) . −− . . . i nd v - . ( ) . . . −− . i n f r - ( ) . −− . −− . m a cc ( ) . . . . . m . ( ) . . . −− . pp i - . ( ) −−−− . . . r e a l c ( ) . −− . . . r p i - . ( ) −−−− . −− . rrr - . ( ) . . −− . s h i b o r - ( ) . . . −− . t a x r . ( ) . . . . . v i x . ( ) . −− . . . go l d . ( ) . −− . −− . il . ( ) . −− . . . a t h e s t e p w i s e l og i s t i c r e g r e ss i o n i s a d o p t e d . T h e p - v a l u e i s l a b e ll e d i n t h e b r a c k e t . b t h e n o i s e - s i g n a l r a t i o f o r s o m e v a r i a b l e i s e i t h e r n o t a v a il a b l e o r i nfin i t y ( I n f ) s i n ce t h e d i v i d e r ( o f t h e l a s tt i m e p o i n t) v a l u e i s o r e x t r e m e l y a pp r oa c h i n g t o ze r o . c f o r n e u r a l n e t w o r k s m o d e l e s t i m a t i o n , t h e i m p o r t a n ce v a l u e b e l o w . % w ill n o t b e d i s p l a y e d . d v a r i a b l e s t h a t a r e a ss e ss e d t o b e u tt e r l y u s e l e ss w ill n o t b ec a l c u l a t e d t h e i m p o r t a n ce i n X G B oo s t , a nd t h e v a l u e w ill b e t r a n s f o r m e d t o p e r ce n t ag e o f % e b o t h t h e i m p o r t a n ce f o r n e u r a l n e t w o r k s a nd t h e a tt e n t i o n w e i g h t f o r a tt e n t i o n - L S T M h a v e b ee n t r a n s f o r m e d t o p e r ce n t ag e ,i. e . t h ee a c h w e i g h t v a l u e t i m e s % . a b l e : E s t i m a t e d c o n t r i bu t i o nd e g r ee o ff a c t o r v a r i a b l e s f o r c u rr e n c y m a r k e t :l o n g - t e r m p r e d i c t i o n . C o e f . L R N S R K L R I m p . NN M D A R F I m p . X G B oo s t W g t . A tt n L S T M ss e c - . ( . ) . . . . . ss e c r −− . −− . −− . s e z - . ( . ) . . . −− . s e z r −− . −− . −− . f r x −− . . . −− . f r x r −−−− . . −− . f r x r e s −− . . . −− . d i s r −− . . . . . i n t r −− . −− −− . b a l g −− . . . −− . cc i −− . . . −− . c p i −−−− . . . . c o m d g −− . . . . . d e b g . ( . ) . −− . −− . d o m c −− . . . . . d o m g −− . −− . . . fi x a −− . −− . . .
448 g dpp - . ( . ) . −− . −− .
475 g dpp −− . . . . .
040 g dp c −− . . . −− . i m e x −− . −− . −− . i nd g −− . . . . . i ndp −− . −− . −− . i nd v −− . −− . −− . i n f r −− . −− . −− . m a cc −− . . . . . m - . ( . ) . −− . −− . pp i - . ( . ) . −− . −− . r e a l c −− . . . . . r p i . ( . ) . −− . −− . rrr . ( . ) . . . . . s h i b o r . ( . ) . −− . −− . t a x r −− . −− −− . v i x −− . . . . .
795 go l d −− . . . −− . il −− . . . −− . a b l e : E s t i m a t e d c o n t r i bu t i o nd e g r ee o ff a c t o r v a r i a b l e s f o r s t o c k m a r k e t : s h o r t - t e r m p r e d i c t i o n . C o e f . L R N S R K L R I m p . NN M D A R F I m p . X G B oo s t W g t . A tt n L S T M ss e c - . ( E - ) . . . . . ss e c r - . ( E - ) . −− . . . s e z . ( E - ) . . . . . s e z r - . ( E - ) . −− . . . f r x −− . . . . . f r x r −−−−−− . . . f r x r e s −− . . . −− . d i s r - . ( E - ) I n f −− . −− . i n t r ( . ) i n f −− . −− . b a l g - . ( E - ) . . . . . cc i . ( . ) . . . . . c p i ( E - ) −− . . −− . c o m d g577 . ( E - ) . −− . . . d e b g - ( E - ) . −− . −− . d o m c . ( E - ) . −− . . . d o m g - . ( E - ) . . . −− . fi x a131 . ( E - ) . −− . . . dpp . ( E - ) . −− . −− . dpp −− . . . . . g dp c - . ( E - ) . . . . . i m e x . ( E - ) . . . . . i nd g - ( E - ) . . . −− . i ndp - . ( E - ) . −− . . . i nd v - . ( E - ) . −− . . . i n f r - ( E - ) . . . −− . m a cc . ( E - ) . −− . −− . m . ( E - ) . −− . −− . pp i - . ( E - ) −− . . . . r e a l c - . ( E - ) . . . . . r p i - ( E - ) −− . . . . rrr . ( E - ) i n f . . −− . s h i b o r −− . −− . −− . t a x r - . ( . ) . −− . . . v i x −− . −− . −− . go l d - . ( . ) . . . . . il . ( . ) . −− . . . a b l e : E s t i m a t e d c o n t r i bu t i o nd e g r ee o ff a c t o r v a r i a b l e s f o r s t o c k m a r k e t :l o n g - t e r m p r e d i c t i o n . C o e f . L R N S R K L R I m p . NN M D A R F I m p . X G B oo s t W g t . A tt n L S T M ss e c −− . . . . . ss e c r −− . −− . −− . s e z −− . . . −− . s e z r −− . −− . . . f r x - ( . ) . . . . . f r x r −−−−−− . . . f r x r e s - . ( . ) . −− . −− . d i s r −−−−−− . −− . i n t r −− . −− −− . b a l g −− . . . . . cc i −− . . . −− . c p i −−−−−− . −− . c o m d g61 . ( . ) . . . −− . d e b g −− . −− . −− . d o m c −− . −− . . . d o m g −− . . . −− . fi x a −− I n f . . −− .
840 g dpp −− . −− . −− . dpp −− . . . −− .
689 g dp c −− . . . −− . i m e x −− . . . −− . i nd g - . ( . ) . . . −− . i ndp −− . −− . −− . i nd v −− . −− . . . i n f r −− . . . . . m a cc −− . −− . −− . m - . ( . ) . . . −− . pp i −− . . . −− . r e a l c −− . . . . . r p i −− . . . −− . rrr −−−−−− . −− . s h i b o r −− . . . −− . t a x r −− . −− . . . v i x −− . −− . −− .
258 go l d −− . . . . . il - . ( . ) . . . . . . Conclusions This paper contributes to uniformly reorganize the debating arguments on constructing early warning sys-tems to predict financial crises in a full comprehending way to compare two essential components of crisisidentifier and crisis predictive models in a unified frameworks, and discuss the variation of leading factors’ link-age to sign the market-specific crisis as the deep-going inspection is demanded by policy makers and practitionersto give adjustment and further diminish risks that potentially drive the economic downturn.We experiment a full mixing of hybrid EWS models, including classic technical quantified index and Markovswitching ARCH model based crisis classifiers, and traditional econometric and state-of-art machine learningbased predictive models, on Chinese currency and stock markets in the past twenty-four years daily and monthlydata, and mainly get three-fold results. First and foremost, the argument of crisis being predictable seems not bepossible to sink but float, even wander, in the debating pool, as the market endogenous instability is proven to beinferred from sufficient forewarning data sources given the modern blossoming powerful predicting techniques.Second, the crisis variable definition should be diversified for a varied predicting period and the SWARCHclassified crisis observations is statistically examined more effective as it distinguishes the price index volatilitydynamics into several state levels, such as low and high, or low, medium and high, according to the amplitude offluctuations, and elastically adjusts the value of threshold to augment the crisis identifying flexibility. Third, theSWARCH with automatically optimized threshold combined deep neural networks models cluster outperformother EWS combinations, more specifically, in the view of predicting power, it show greatest robustness givenhighest precision and widest precautionary periods, and in the practical perspective, it has been back tested tosucceed most in terms of lowering the EWS involved portfolio returns instability, especially for daily exercising.Last but not least, the leading factors’ variation, the point has yet been discussed in previous studies but beginsto start up in our study, is assignable for market-specific crisis prediction. Besides, the predicting term isinvestigated to negatively effect the quantity of included leading factors, in other words, shorter the term is,more factors will be drawn as leading indicators to foresee crises, albeit in a somewhat overloaded informationdisturbance in the real world.According to the results, we conclude major implications in the practical application perspective. First ofall, the necessity of introducing an effective classifier to the crisis prediction is verified in the study, since suchcrisis identification technique, for example the SWARCH with dynamically optimized cutoff model, is capableof, not only weakening the impact from imbalanced sample distribution, as Chatzis et al. (2018) previouslymentioned, but boosting the warning system’s predicting power as well. Second, the machine learning modelbased EWS cluster, though often bears the criticism on over-parameterization and weak interpretability (of innercell parameters and structural weights), does give compelling performance on crisis predicting effectiveness andlowering investment risk in empirical application. It is though hard to dogmatically assert that machine learningbased warning systems generally dominate the traditional models, especially considering there should be a greatdiversity among different types of financial crises, at least, proportional to the market information symmetry,machine learning, especially deep learning, base early warning system should be designated as long as the datasources are abundantly acquired. Third, there is a unilateral contagious effect across the stock and currencycrises, that is the exchange rate dynamics can be referred as a precognition factor to forewarn the stock marketcrisis, but the reverse risk transmission from stocks to currency is yet revealed by evident proofs. Thus, in final,for decision makers, constructing an early warning system is required to considerately examine whether theclassification methodology is competent to fully reflect the market fluctuation according to their each volatilityrules, in addition to select the most suitable model in line with different objectives, such as either solely pursuinghigh predicting accuracy or ensuring the output reliability, and either searching for striking factors to crises orimplementing mixed aims. On the other hand, in the investor’s view, especially for short-term investors withlow risk aversion, the requirements to model producing timely and effective warning signals share a greaterpriority considering they may undertake higher risk of loss in crises, therefore, referring forewarned results froman ensemble of EWS models probably keep them safer than solely relying on one.The concluded remarks in the study do not aim for depriving the privilege on open questioning and furtherexploring the predicting system generalizations, but to achieve the extensibility on the crisis predictabilityarguments and the comprehensiveness on the early warning system predicting precision and practical value.This study suggests, among a broad aggregation of crisis forecasting methodologies, the crisis identification thatrelies on the volatility regime switching frameworks partnering with the predictive models that entrust stylizedmachine learning techniques (especially deep neurons networks), seem to earn rather more accreditation thantraditional means under the high-frequency data preliminaries. Further efforts, based on current inspiringfindings, are thus worthy of being paid in following aspects: (i) at the methodological level, the diversity ofmachine learning methods are encouraged to be explored, especially in arithmetic and structures design; (ii) atthe computational level, as the computing capacity is continuously boosting, precisely forecasting the timing34f crises or crashing events will no longer be unattainable goal if the real-time computation can be introduced;(iii) at the data level, either cross-section or cross-country is yet discussed but highly valued in research on thecrisis recurrences for regional and global economies as long as the database accessing is not restricted.
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The table is being processed and will be pasted later... ppendix II (a) Exchange rate and SSEC index dynamics.(b) FPI and CMAX identified crises.(c) SWARCH opt identified crises.Figure 7: Visualized TQI and SWARCH opt identified crises on full samples for monthly data. (a) plots the exchange rate andSSEC index including their change return dynamics (under the price index). The grey dotted lines in (b) label the normalized FPIindex and CMAX index and that in (c) label the filtering probability value extracted from AR(1)-SWARCH(2,1). Red solid linesrepresent the identified crises.identified crises on full samples for monthly data. (a) plots the exchange rate andSSEC index including their change return dynamics (under the price index). The grey dotted lines in (b) label the normalized FPIindex and CMAX index and that in (c) label the filtering probability value extracted from AR(1)-SWARCH(2,1). Red solid linesrepresent the identified crises.