A Regulated Market Under Sanctions: On Tail Dependence Between Oil, Gold, and Tehran Stock Exchange Index
AA Regulated Market Under Sanctions.On Tail Dependence Between Oil, Gold, andTehran Stock Exchange Index
Abootaleb Shirvani, Dimitri Volchenkov
Abstract
We demonstrate that the tail dependence should always be taken intoaccount as a proxy for systematic risk of loss for investments. We provide the clearstatistical evidence of that the structure of investment portfolios on a regulated marketshould be adjusted to the price of gold. Our finding suggests that the active barteringof oil for goods would prevent collapsing the national market facing the internationalsanctions.
Keywords:
Regulated markets, Tehran Stock Exchange, Financial Econometrics,Tail Dependence.
Since 1979, the UN Security Council and the United States regularly passed a numberof resolutions imposing economic sanctions on Iran regarding supporting for Iran’snuclear activities [1]. Over the years, sanctions have taken a serious toll on Iran’seconomy and people, as well as resulted in the increasing government control overthe forces of supply and demand and prices in Iran.Oil price changes have a significant effect on economy since oil prices directlyaffect the prices of goods and services made with petroleum products. Increases inoil prices can depress the supply of other goods, increasing inflation and reducingeconomic growth [2]. Being an energy superpower, Iran has an estimated 158 blnbarrels of proven oil reserves, representing almost 10% of the world’s crude reservesand 13% of reserves held by the Organization of Petroleum Exporting Countries [3].The Petroleum industry in Iran accounted for 60% of total government revenues and80 % of the total annual value of both exports and foreign currency earnings in 2009
Department of Mathematics and Statistics, 1108 Memorial Circle, Lubbock, TX 79409, USA,e-mail: [email protected],[email protected]. a r X i v : . [ q -f i n . S T ] N ov Abootaleb Shirvani, Dimitri Volchenkov [4]. The oil price volatility should strongly affect the Tehran Stock Exchange index(TSE).Gold is one of the basic assets ensuring stability of national currency. In aneconomic downturn, people tend more towards gold as a safe asset while reducingtheir investments that leads to deeper economic downturn [5]. Iran’s gold bar andcoin sales tripled to 15.2 tons in the second quarter of 2018, the highest in four yearsas announced by the World Gold Council. According to Bloomberg, Iran’s demandfor gold bars and coins may remain strong for the rest of the year and even increaseas the US reimposes sanctions [6]. The gold price volatility should strongly affectthe Tehran Stock Exchange index (TSE).
Fig. 1
Daily log-returns for the period from 28/02/2005 to 14/11/2018 for the (a.) Tehran StockExchange; (b.) Gold; (c.) Crude Oil price.
The main objective of this paper is to estimate stochastic dependence betweenthe daily log-returns for oil and gold and TSE by applying the copula method forconstructing non-Gaussian multivariate distributions and understanding the relation-ships among multivariate data. We also assess the degree of dependence betweenextreme events on the national oil and gold markets and TSE. Although the linearcorrelation analysis shows positive correlations between the quantities of interest,the copula method indicates that the degree of dependence between oil and TSE isweak while there might be a significant left tail dependence between TSE and goldthat can be thought of as a proxy for systemic risk of default.
Regulated Market Under Sanctions 3
We use daily data for the closing Euro Brent Crude-oil price (in US dollars pershare) and closing gold historical spot price (in US dollars per ounce) obtained fromthe Historical London Fix Prices [7]. The daily adjusted closing price for the TSEwere taken from the official web site of the Tehran Stock Exchange [8]. The timestamps of TSE prices were converted from the Persian to Western dates. The dailylog-returns of data time series (for gold, oil, and TSE) for the period from 28/02/2005to 14/11/2018 are plotted in Fig. 1.In Sec. 2, we provide a literature review on the tail dependence between oil,gold, and stock market indices in Iran and worldwide. In Sec. 3, we give a briefintroduction to the copula method. Our main contribution is explained in Sec. 4. Weapply the tail copula method to investigate the dependence of joint extreme eventsfor the gold and oil prices and TSE index. The standard ARMA-GARCH model isused to estimate the marginal distributions and to filter out the serial dependenceand volatility clustering in the data. Several copula models are implemented to thestandardized residuals of each series. We estimate and model the tail dependencefor the gold and oil prices and TSE index empirically and theoretically. We thenconclude in the last section.
The impact of crude oil and gold prices on financial markets has been broadlydiscussed in the literature. Hamilton (1983) had shown that the oil price has anessential impact on the economy and its volatility leads to a stock market pricechange [9]. Kling (1985) applied the Vector Autoregressive (VAR) model to assessthe impact of oil price movement on the S&P 500 Index and five US industries [10].Huang et al. (1996) considered the relationship between log-return of oil and US stockmarket, by using VAR model [11] and demonstrated that the oil futures might affectthe stock returns of oil companies. Sadorsky (1996) used the unrestricted VAR modelwith generalized autoregressive conditional heteroskedasticity (GARCH) model toshow the negative impact of increasing oil prices on the US stock market [12].Cai et al. (2001) observed that the GDP per capita and the inflation rate have asubstantial effect on the gold price volatility [13]. Baryshevsky (2004) observed thehigh inverse correlation between real stock returns and the ten years average rate ofgold [14]. Nandha and Faff (2008) reported the strong correlation between oil pricesand the stock market in oil exporting countries [15].Miller and Ratti (2009) found that after 1994 the long-term response of marketindices to the oil price shocks was negative [16]. Baur and Mcdermott (2010) studiedthe impact of gold price on the financial market during 1979-2009 and observed thatgold acts as a hedge in the stock market of the US and most European countries [17].The empirical findings of Batten et al. (2010) was that volatility of the gold returnhas a substantial impact on financial market returns [18].Recently, several authors have applied time series models and the copula methodto measure co-movements in the tails of the multivariate distributions. Bharn and
Abootaleb Shirvani, Dimitri Volchenkov
Nikolovann (2010) considered the relationship between oil price and stock marketsin Russia by applying the exponential GARCH model [19]. Fillis et al. (2010)studied the time-varying dependence between oil price and stock market in differentcountries during 1997-2009 by applying the DCC-MGARCH model [20]. Arouri etal. (2011) measured the degree of dependence between the oil price shocks and theGulf Cooperation Council (GCC) stock market by the VAR-GARCH model [21].Jäschke et al. (2012) modeled large co-movements of the commodity returns byapplying the copula method to extreme events on the energy market [23].Applying the ARJI-GARCH model, Chang (2012) observed that the tail depen-dence between crude oil spot and the future market is time-varying and asymmetric[22]. With the use of Archimedean copulas, Nguyen and Bhatti (2012) found nosignificant evidence of tail dependence between the stock market indices and oilprice changes in China and Vietnam [24]. Aloui et al. (2013) implemented threeArchimedian copulas to measure the significant impact of crude oil price changeson the stock market indices of Gulf Cooperation Council economies [25].Mensi et al. (2013) studied volatility transmission across the gold, oil, and equitymarkets and demonstrated the effect the gold and oil price variations have on the S&P500 index [26]. The copula method had been used for exploring the tail dependencebetween the financial and credit default swap markets by Silva et al. (2014) [27].Arouri et al. (2014) observed the significant impact of gold price volatility on theChinese stock market in 2004 - 2011 by applying the VAR-GARCH model [28].Using the quantile regression method, Zhu et al. (2016) found the strong dependenceat the upper and lower tails between the crude oil prices and the Asia-pacific stockmarket index for 2000-2016 [29]. Siami-Namini and Hudson (2017) examined thevolatility spillover from the returns on crude oil to the commodities returns by usingthe Autoregressive (AR) model with the Exponential GARCH model [30], in theperiod from Jan 2006 to Nov 2015. Trabelsi (2017) studied the asymmetric taildependence between international oil market and the Saudi Arabia sector indicesin 2007-2016 [31]. Hamma et al. (2018) applied the copula method and ARMA-GARCH-GDD model to analyze the dependence between stock market indices ofTunisia and Egypt and the crude oil price in 1998-2013 [32].Few scholars have investigated the dependence between the oil and gold pricesand the stock market index in Iran. Foster and Kharazi (2008) found no significantcorrelation between the variations of oil price and TSE in 1997-2002 [33]. Applyingthe ARMA-copula method, Najafabadi et al. (2012) observed that the gold and oilprice changes might weakly influence TSE [34]. Shams and Zarshenas (2014) agreedon that there is no significant evidence of dependence between the oil and gold pricevariations and the TSE index [35].
We investigate time series of the daily log-returns,
Regulated Market Under Sanctions 5 r t = log (cid:18) S t S t − (cid:19) , (1)for the closing prices of an asset S t . The ARMA-GARCH model [36, 37] is a standard tool for modeling the conditionalmean and volatility of time series. The GARCH model captures several importantcharacteristics of financial time series, including the heavy tail distribution of re-turns and volatility clustering. The ARMA-GARCH model filters out the linear andnonlinear temporal dependence in bi-variate times series, r t = µ + (cid:205) pt = i ϕ i ( r t − i − µ ) + (cid:205) qj = θ j a t − j + a t , a t = ε t σ t , ε t ∼ iid ,σ t = γ + (cid:205) km = β m σ t − m + (cid:205) ln = α n a t − n . (2)where r t is the assets return, µ in constant term, p and q are the lag orders ofARMA model, k and l are the lag orders of GACH model, σ t = v ar ( r t | F t − ) is theconditional variance during the period t , F t − denotes the information set consistingof all linear functions of the past returns available during the time period t − ε t is the standardized residual during the time period t , which are iid with zero meanand unit variance; a t is referred to the shock of return during the period t ; γ ≥ θ j { j = , , ..., q } , ϕ i { i = , , ..., p } , α n ≥ { n = , , ..., l } and β m ≥ { m = , , ..., k } are the parameters of the model estimated from the data. A copula is a multivariate probability distribution for which the marginal-probabilitydistribution of each variable is uniform [38]. Application of the copula method todescription of the dependence between random variables in finance is relatively new.In line with Sklar’s Theorem [38], every cumulative bivariate distribution F withmarginal distributions F and F can be written as F ( x , x ) = C ( F ( x ) , F ( x )) , (3)for some copula C , which is uniquely determined on the interval [ , ] .Conversely, any copula C may be used to design a joint bivariate distribution F from any pair of univariate distributions F and F , viz., C ( u , v ) = F (cid:16) F − ( u ) , F − ( v ) (cid:17) , Abootaleb Shirvani, Dimitri Volchenkov where F − and F − are the quantile functions of the respective marginal distribu-tions. If we have a random vector X = ( X , X ) , the copula for their joint distributionis C ( u , v ) = P ( U ≤ u , V ≤ v ) = F (cid:16) F − ( u ) , F − ( v ) (cid:17) , (4)for all u , v ∈ [ , ] .We also use the survival copula ¯ C that links the joint survival function ¯ F ( x ) = − F ( x ) to the univariate marginal distribution, viz.,¯ C ( u , v ) = ¯ C (cid:0) ¯ F ( u ) , ¯ F ( v ) (cid:1) = Pr ( X ≥ u , X ≥ v ) . (5)Following [39], we can write survival copula function as¯ C ( u , v ) = Pr ( U ≥ − u , V ≥ − v ) = ¯ F (cid:16) F − ( − u ) , F − ( − v ) (cid:17) . (6) The Kendall and Spearman rank correlation coefficients of two variables, X and X , with the copula C ( u , v ) are given by τ ( X , X ) = ∫ ∫ C ( u , v ) dC ( u , v ) − , (7)and ρ S ( X , X ) = ∫ ∫ C ( u , v ) du d v − , (8)respectively.Let the distribution of X and X denote by F and F . The following relationexists between Spearman’s rank and linear correlation coefficients: ρ s ( X , X ) = C ( F ( x ) , F ( x )) , (9)where ( u , v ) = ( F ( x ) , F ( x )) .The relations between Kendall’s Tau and Spearman’s rank correlation coefficientsand the coefficient of linear correlations in the Gaussian and Student’s t-copulas are Corr ( X , X ) = sin (cid:16) π τ (cid:17) , (10) Corr ( X , X ) = sin (cid:16) π ρ s (cid:17) . (11)Both ρ s and τ may be considered as a measure of the degree of monotone depen-dence between random variables, whereas the linear correlation coefficient measuresthe degree of linear dependence only. Since τ and ρ s measure the dependence incentered data, they are often insufficient to estimate and describe the dependence Regulated Market Under Sanctions 7 structure of extreme events. Hence, according to Embrechts et al. (1999) [40], it issignificantly better to use the tail copula method than the linear correlation coeffi-cient to characterize the dependence of extreme events. In their opinion, one shouldchoose a model for the dependence structure that reflects more detailed knowledgeof the value at risk, and the tail copula method is an excellent tool for managing risksagainst concurrent events.The standard way to assess tail dependence is to look at the lower and upper tailcoefficients denoted by λ l and λ u , respectively, where λ u quantifies the probabilityto observe a large X value given the large value of X . Similarly, λ l is a measure thatquantifies the probability to observe a small X value, assuming that the value of X is small. Let X i ∼ F X i and the probability α ∈ ( , ) then the upper tail coefficientis: λ u ( X , X ) = lim α → Pr (cid:16) X ≥ F − ( α ) | X ≥ F − ( α ) (cid:17) , (12)and similarly λ l ( X , X ) = lim α → Pr (cid:16) X ≤ F − ( α ) | X ≤ F − ( α ) (cid:17) . (13)On the one hand should λ l ( X , X ) = ( λ u ( X , X ) = ) then X and X are said to belower (upper) asymptotically independent. On the other hand should λ l ( X , X ) > ( λ u ( X , X ) > ) , then the small (large) events tend to happen coherently, and X and X are lower (upper) tail dependent.According to Jäschke (2012) [23], the Value-at-Risk (VaR) is closely related tothe concept of tail dependence. Tail dependencies can be considered as the degreeof likelihood of an asset return falling below its VaR at the certain level α whenthe other asset returns have fallen below its VaR at the same level. In general, λ l and λ u (like the other scalar quantities) describe a certain level of dependence intails. However, in our analysis, we need to describe the general framework of taildependence for bi-variate distributions.In the general framework of tail copulas, the dependence structure of extremeevents in bi-variate distributions, independently of their marginals, is represented bytail dependence (see Schimtz and Stadtmüller (2006) [41] for more details).The lower and upper tail dependence associated with X and X are Λ L ( X , X ) = lim t →∞ t C (cid:16) x t , x t (cid:17) , (14) Λ U ( X , X ) = lim t →∞ t ¯ C (cid:16) x t , x t (cid:17) (15)provided the above limits exist everywhere on IR + : = [ , ∞) . According to Schimtzand Stadtmüller (2006) [41], the estimation of tail dependence is a nontrivial task,particularly for a non-standard distribution that is why we consider the tail coefficientas a measure of the tail dependence. The tail coefficient is a specific case of taildependence, and we have λ l = Λ L ( , ) and λ u = Λ U ( , ) . Abootaleb Shirvani, Dimitri Volchenkov
First, we perform the Ljung-Box Q -test [42] to examine the presence of autocor-relation in log-returns and the presence of heteroskedasticity in squared log-returnof each data set for lags 5 and 10. The p -values ( p < . ) indicate that the log-return of data (on gold, oil, and TSE) are autocorrelated in each times series. Thereare significant heteroskedasticity effects, since all p -values are less than 0.01. Thehypothesis of independent and identically distributed data is therefore rejected.Second, to investigate the multiple co-integration relationships among the gold,crude oil, and TSE time series, we apply the Engle-Granger co-integration test [36,37]. The obtained p -values ( p = . , p = . ) reject the null hypothesisof no co-integration among the time series. The test result indicates that there is along-run relationship among the variables, and they share a common stochastic drift.Third, the linear and nonlinear temporal dependencies in bi-variate times seriesshould be filtered out by applying the ARMA-GARCH model [36, 37]. We tried theARMA-GRACH model with various lags and different distributions to select theoptimal model for each times series. Namely, we have tested the normal, Student’s t,generalized error, skewed Student’s t, and generalized hyperbolic distributions.To examine the presence of long memory dependence in each times series, weperform the fractional ARMA(1,d,1)-GARCH(1,1) test. The results of all tests aregiven in Tab. 1.The test p -values for gold and oil log-returns ( p ≥ . ) ) demonstrate no longmemory dependence in oil and gold times series. However, the very small p -valuefor TSE log-return ( p = . ) shows that there is a long memory dependence in theTSE time series. The fractional exponent ( d (cid:39) . ) of the shift operator ( − B ) confirms the presence of long memory dependence in the TSE log-returns.Fourth, we have evaluated all possible ARMA-GARCH models ( p ≤ , q ≤ , k ≤ , l ≤
2) with the use of the R-Package "rugarch" [43] by examining i.) AkaikeInformation Criterion (AIC); ii.) Bayesian Information Criterion (BIC) [36, 37]; iii.)the statistical significance test of model parameters at the 5% -level; iv.) lack ofautocorrelation; v.) lack of heteroskedasticity in standardized residuals of each timeseries for lags 5 and 10.Fifth, to evaluate the density of standardized residuals (innovations) in each timeseries, we apply probability integral transform method following [44]. This method is
Table 1
Long memory test in TSE, Oil, and Gold log-returnData FARIMA(1, d ,1)-GARCH(1,1) d p -valueTSE 0.142 0.000Oil 0.042 0.059Gold 0.050 0.102 Regulated Market Under Sanctions 9 based on the relation between the sequence of densities of the standardized residuals, p t ( z t ) , and its integral probability transform, y t = ∫ z t −∞ p t ( u ) du . (16)We evaluate the densities of the standardized residuals by assessing whether theprobability integral transform series, { y t } mt = , are iid U ( , ) . The non-parametricKolmogorov-Smirnov test is the easiest way to check the uniformity of y t ’s [45].By comparing all criteria and evaluating the densities of the standardized resid-uals, the obtained time series models are the FARIMA ( , . , ) - GARCH ( , ) model with the Standardized Generalized Hyperbolic Distribution (SGHYD), theARMA ( , ) − GARCH ( , ) model with Student’s t-distribution with v = . ( , ) model with SGHYD, for TSE, gold, andoil time series, respectively. The estimated parameters of each model obtained by Table 2
Maxmium likelihood estimation, standard errors, and estimations of model parametersin FARMA ( , ) -GARCH ( , ) with SGHYD for TSE, the ARMA ( , ) -GARCH ( , ) model withStudent’s t-distribution for oil, and the GARCH ( , ) model with SGHYD for gold. Parameter
TSE log-return Oil log-return Gold log-returnEsitmation Std. error Esitmation Std. error Esitmation Std. error
ARMA-GARCH model ϕ θ — — -0.7850 0.2239 — — α β d -(arfima) 0.1331 0.0203 — — Distribution ν (DF) 0.2500 0.0158 3.3629 0.2743 0.2500 0.0253 ζ -0.0327 0.0613 — — 0.0035 0.0187 η -1.1811 0.1183 — — 0.3665 0.0657 using the maximum likelihood methods are given in Tab. 2.To study autocorrelation and conditional heteroskedasticity in each residual timeseries, we have shown the QQ plots, and correlograms for z t and z t , for eachstandardized residual series in Fig. 2. The apparent linearity of the QQ-plots showsthat the corresponding distributions are well-fitted.The parameters for each model were estimated by the maximum-likelihoodmethod and all parameters are found significant at the 5% -level. Since the p -valuesin the Ljung-Box Q-tests are less than 0 .
01, there is no significant autocorrelationand heteroskedasticity of the standardized residuals at the 5%-level for each timeseries.For evaluating the forecast densities of each model, first we calculate the { y t } mt = for each standardized residual sets associated with gold, oil and TSE. Then, we testthat y t ’s are iid U ( , ) by the Kolmogorov-Smirnov and Sarkadi-Kosik tests [46] Fig. 2
QQ plot and correlogram of ACF of standardized residuals and ACF of squared standardizedresiduals for (a). TSE log-return, (b). Oil log-return, (C) Gold log-return with the use of the R-package "uniftest" [47]. The p -values ( p ≥ .
05) indicate that y t ’s are iid U ( , ) at the 5%-level.We conclude that the obtained distributions are well fitted.Therefore, the optimal ARMA-GARCH model for the oil log-returns is Regulated Market Under Sanctions 11 O t = . + . O t − − . a t − + a t , a t = o t σ t , o t iid ∼ t ( ν = . ) ,σ t = . o t − + . σ t − . (17)The best ARMA-GARCH model for the gold log-returns is G t = . + a t , a t = g t σ t , g t iid ∼ SGHY D ( . , . ) ,σ t = . g t − + . σ t − . (18)Finally, the optimal model for the log-returns for TSE is ( − B ) . S t = . + . S t − + a t , a t = s t σ t , s t iid ∼ SGHY D (− . , . ) ,σ t = . s t − + . σ t − . (19)where B is back-shift operator. The rugarch [43] package performs GHYD parameterestimations using the ( η, ζ ) parametrization (SGHYD), after which a series of stepstransform those parameters into the ( µ, α, β, δ ) while at the same time including thenecessary recursive substitution of parameters in order to standardize the resultingdistribution. In this section, we model the dependence structure between the log-returns of oil,gold, and TSE denoted by O t , G t , and S t , respectively, by the copula method. Wehave already shown that the O t , G t and S t are time-varying dependence series.We applied the time series model to filter out time-varying dependence and obtainstandardized residuals for gold, oil, and TSE, denoted by g t , o t , and s t , respectively.We work with the iid standardized residuals for each time series.Deheuvels et al. (1979) [48] introduced the empirical copula based on the rankcorrelation. An initial approach to calculate the empirical copula function is toestimate the distribution function of residuals based on the empirical distributionfunction F X , F X ( x ) = T + T (cid:213) i = ( X i ≤ x ) , (20)where ( A ) denotes the indicator function of the set A . The quantities F X ( x i ) and F Y ( y i ) as given by (20) are the ranks of X i and Y i normalized by T + o t , g t , and s t are transformed to the rank-based variables by u t = rank ( o t ) T + , v t = rank ( g t ) T + , w t = rank ( s t ) T + . (21) The domain of empirical copula, ( u , v ) ∈ [ , ] [49], is formed by all normalizedranks, (cid:8) T + , T + , ..., TT + (cid:9) , for each residual set. The best sample-based empiricalcopula is then defined by C u ( u , v ) = T T (cid:213) t = ( U t < u , V t < v ) , (22)and the empirical survival copula is¯ C u ( u , v ) = T T (cid:213) t = ( U t ≥ u , V t ≥ v ) . (23)Before using the obtained copulas, we have estimated the Spearman ρ and Kendall τ rank correlation coefficients from the normalized ranks (see Tab. 3). The obtainedcoefficients show that the dependence between oil and TSE is very weak, but thecorrelation between gold and TSE is significant. The dependence between gold, oil, Table 3
Correlation between ranks of standardized residual of gold, oil and TSEMethod Kendall SpearmanGold Oil Gold OilTSE 0.111 0.017 0.162 0.026 and TSE was also assessed by applying the multivariate independent test [50]. Theobtained p -value ( p = . ) at the 5% level rejects the hypothesis of independenceof these variables. We conclude that the Spearman and Kendall’s correlations cannot measure the entire dependence between the quantities of interest.Now we determine the optimal copula model to describe the dependence structureof the joint distributions. We consider both theoretical (parametric) C and empirical(non-parametric) C u methods. We fit several copula families [Independent, Gaus-sian, Student’s t, Clayton, Gumbel, Frank and Joe] on standardized residuals. Theunknown copula parameter θ is obtained by the inverse τ method , i.e., by solving theequation (11) for the value ˆ τ estimated from the data with the use of the R-package’VineCopula’ [51]. The parameter θ controls the strength of dependence in each cop-ula family; its values are collected in Tab. 4. The significance of each fitted copulais examined by the goodness of fit test with the use of Cramer-Von-Mises statistics[52]: S t = T (cid:213) t = (cid:16) C t ( u t , v t ) − C ˆ θ t ( u t , v t ) (cid:17) . (24)The corresponding p -value is obtained by the bootstrapping method (see [53] fordetails). We have evaluated each copula family with respect to the following three Regulated Market Under Sanctions 13 criteria: i.) the high p -value of the goodness of fit test; ii.) the AIC; and ii.) the BICvalues. The obtained values are given in Tab. 4. Table 4
The copula parameters and goodness-of-test results for the different copula families.Oil and TSE Gold and TSECopula ˆ θ AIC BIC p -value ˆ θ AIC BIC p -valueIndependent 0.79 0.00Gaussian 0.037 -2.249 3.822 0.83 0.174 -82.875 -76.803 0.02t 0.034 6.544 18.688 0.04 0.173 -66.765 -54.622 0.00Clayton 0.028 -0.451 5.621 0.63 0.161 -44.561 -38.489 0.40Gumbel 1.016 -1.285 4.787 0.75 1.080 -50.448 -44.377 0.07Frank 0.151 -0.053 6.019 0.34 1.003 -80.859 -74.788 0.00Joe 1.019 -0.666 5.405 0.76 1.080 -19.940 -13.868 0.63a.) b.) We conclude that the Student’s t copula is not appropriate for modeling thedependence between oil and TSE (as p -value ≤ . p -values for gold and TSE also reject the Independent, Frank, and t copula families atthe 5% level. For any other candidates, the p -value can not reject the null hypothesis.The Gaussian copula is a candidate for the optimal model describing the thedependence between oil and TSE, with the smallest AIC and BIC values, and thehighest p -value among all other candidates.Due to zero p -value, the Frank copula is not a good fit for the description ofdependence between gold and TSE although the values of AIC (− . ) and BIC (− . ) are the smallest ones. A copula family with the non-trivial tail coefficientsand higher p -value goes over other families in explaining the entire dependencebetween gold and TSE. Therefore, we have selected the Joe copula as a propercandidate because of its higher p -value ( . ) and the smaller AIC and BIC valuesover the Clayton copula even though the lower tail dependence coefficient in Joecopula is zero. Jäschke et al. have shown that the goodness-of-fit test alone does not necessarilyprovide an appropriate model for tail dependence, because it is based on minimizingthe distance between the observed ranks model and parametric model over the wholesupport of the distribution [23]. They suggested applying the tail copulas conceptfor capturing dependence in the tail of distribution to improve the effectivenessof fitted copula. The non-parametric estimators are defined up to a scaling factor k = , , ..., T chosen by a statistician [41], for the lower tail copula,ˆ Λ L ( x , y ) = Tk C u (cid:18) k xT , k y T (cid:19) = k T (cid:213) t = (cid:18) u t ≤ k xT + , v t ≤ k y T + (cid:19) , (25) and for the upper tail copula,ˆ Λ U ( x , y ) = Tk ¯ C u (cid:18) k xT , k y T (cid:19) = k T (cid:213) t = (cid:18) u t > T − k xT + , v t > T − k y T + (cid:19) , (26)respectively. Based on the above estimators, they found thatˆ λ l = ˆ Λ L , T ( , ) , ˆ λ u = ˆ Λ U , T ( , ) (27)are the appropriate non-parametric estimators for the upper and lower tail dependencecoefficients.We estimate the lower and upper tail coefficients by using the equations (27. Thevalues of coefficient estimators for tail dependence between oil and TSE, gold andTSE are given in Tab. 5). In the preceding section, our results based on the highest Table 5
Tail dependence coefficient estimators for tail dependence between oil & TSE, gold &TSE for the different copula families. Oil and TSE Gold and TSECopula lower upper lower upperIndependent 0.0000 0.0000 0.0000 0.0000Gaussian 0.0000 0.0000 0.0000 0.0000Clayton 0.0000 0.0000 0.0434 0.0000Gumbel 0.0000 0.0216 0.0000 0.1000Frank 0.0000 0.0000 0.0000 0.0000Joe 0.0000 0.0250 0.0000 0.1005Empirical 0.0000 0.0000 0.0680 0.0000 p -value, the smallest AIC and BIC values have suggested that the Gaussian copulais the optimal one for describing the dependence between oil and TSE. However,the zero values of estimators given in Tab. 5 indicate that there is no significanttail dependence between oil and TSE, in line with the small values of the linearcorrelation coefficients given in Tab. 3. Therefore, we conclude that the independentcopula is the optimal model for describing the dependence between oil and TSE onthe Iranian market.Concerning the tail dependence between gold and TSE, the results of the previoussubsection show that the Joe copula is optimal for describing the dependence struc-ture between gold and TSE. The non-parametric estimators for the upper and lowertail dependence between gold and TSE given in Tab. 5. By comparing the empiricalcoefficients with the parametric tail coefficient of Joe copula, we conclude that theJoe copula, which has the nontrivial upper tail and zero lower tail dependence, cannot well enough explain the risk of extreme events in the tails.From Tab. 5, we see that the Gumbel copula goes over other copula families inexplaining the dependence structure between gold and TSE due to the small AIC Regulated Market Under Sanctions 15 and BIC values. However, comparing the empirical coefficients with the parametrictail coefficients of Gumbel copula, we see that the former is inverse with respect tothe Gumbel ones. Therefore, we should reject the Gumbel copula as well.We conclude that the Clayton copula is the optimal model for describing thedependence structure between gold and TSE on the Iranian market, because thelower tail coefficient is close to empirical while the upper tail is zero. The Claytoncopula has the second highest p -value among the other candidates, and its AIC andBIC values are small comparing to those for others copulas (see Tab. 5). Tails matter!
In our work, we convincingly demonstrate that the standard goodnessmeasures for fitting copulas to data, such as the p -value, AIC/ BIC values, are not thereliable indicators of goodness-of-fit. The tail dependence should always be takeninto account as a proxy for systemic risk by risk managers.Although the small AIC/ BIC values and the goodness-of-fit test assume that theGaussian copula is the good one for representing the dependence structure betweenoil and TSE on the Iranian market, the absence of tail dependence and low correlationbetween these assets disclose that the independent copula is the optimal one for fittingthe data. Again, the small AIC/ BIC values, the goodness-of-fit test, and the high p -value suggest that the Joe copula would be a good data model describing therelation between gold and TSE on the Iranian market. However, our finding revealsthat the Joe copula, which has only an upper tail and no lower tail dependence,fails to describe the tail dependence of gold and TSE properly. The empirical tailcoefficients suggest that the Clayton copula might be a suitable model fitting the dataon gold and TSE well. Watch the gold price!
Our finding has the important implications for risk man-agers and investors, because of it can help them to adjust the structure of theirinvestment portfolios once the gold price changes. Risk managers should reduce theratio of their investments into TSE whenever the gold price is decreasing.
Barter when facing sanctions!
Our finding has also the important implicationsfor policy maker of countries faced international sanctions. The lack of dependencebetween the TSE index and the oil price generating the major foreign currencyrevenue suggests that oil dollars almost do not influence the national market of Iran.Faced with the international sanctions, Iran was turning to barter by offering goldbullion in overseas vaults or tankerloads of oil, in return for food as the financialsanctions had hurt its ability to import basic staples [54]. Those sanctions werenot banning companies from selling food to Iran, but the transactions with bankswere very difficult. Unable to bring in U.S. dollars and euros ahead of the new U.S.sanctions, Iran is open to accepting agricultural products and medical equipment inexchange for its crude oil [55]. A scheme to barter Iranian oil for European goodsthrough Russia, which would then refine it and sell it to Europe as part of mechanism to bypass American sanctions on the Islamic Republic was announced by Europe,China, and Russia along the sidelines of the United Nations General Assembly [56].In the future, we plan to implement the copula method by using rolling windows formodeling the time-varying dependence between gold, oil and TSE in a multivariateframework.
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