Catherine Kyrtsou

Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Applicationof a Noisy Mackey–Glass Equation with Heteroskedastic Errors to theParis Stock Exchange Returns Series

Most recent empirical works that apply sophisticated statistical proceduressuch as a correlation-dimension method have shown that stock returns arehighly complex. The estimated correlation dimension is high and there islittle evidence of low-dimensional deterministic chaos. Taking the complexbehaviour in stock markets into account, we think it is more robust than thetraditional stochastic approach to model the observed data by a nonlinearchaotic model disturbed by dynamic noise. In fact, we construct a model havingnegligible or even zero autocorrelations in the conditional mean, but a richstructure in the conditional variance. The model is a noisy Mackey–Glassequation with errors that follow a GARCH(p,q) process. This model permits usto capture volatility-clustering phenomena. Its characteristic is thatvolatility clustering is interpreted as an endogenous phenomenon. The mainobjective of this article is the identification of the underlying process ofthe Paris Stock Exchange returns series CAC40. To this end, we apply severaldifferent tests to detect longmemory components and chaotic structures.Forecasting results for the CAC40 returns series, will conclude this paper.

Complex Dynamics in Macroeconomics: A Novel Approach

In this work we employ the Recurrence Quantification Analysis (RQA) framework, effective in discovering evidence of non-linear determinism and complex dynamics in short, noisy and irregular signals. We apply RQA to a set of US macroeconomic time series and simulated sequences in order to provide a classification based on topological aspects of their dynamics. Through RQA we can in general obtain useful information on the quality and complexity of the structure of the dynamics in an economy, as this is embedded in its macroeconomic time series.

Evidence for Nonlinear Asymmetric Causality in US Inflation, Metal, and Stock Returns

The purpose of this paper is to propose a version of causality testing that focuses on the role of the sign of the returns on the causality results. We replace the traditional VAR specification used in the Granger causality test by a discrete-time bivariate noisy Mackey-Glass model. Our test reveals interesting and previously unexplored relationships in U.S. economic series, including inflation, metal and stock returns.

New Trends in Macroeconomics

The Propagation of Macroeconomic Shocks: A Dynamic Model with Contracts and Imperfect Competition.- Variable Elasticity of Substitution and Economic Growth: Theory and Evidence.- Financial Intermediation and Economic Growth: A Semiparametric Approach.- Bridging the Gap: Linking Economics and Econometrics.- Revenue Smoothing in an ARIMA Framework: Evidence from the United States.- What VAR Tell us about DSGE Models?.- Ex ante Real Returns in Forward Market Speculation in the Inter-War Period: Evidence and Prediction.- Testing for Fractional Cointegration: The Relationship between Government Popularity and Economic Performance in the UK.- Non-stationarity Tests in Macroeconomic Time Series.- Seasonality, Nonstationarity and the Structural Forecasting of the Index of Industrial Production.- Complex Dynamics in Macroeconomics: A Novel Approach.

Evidence for Neglected Linearity in Noisy Chaotic Models

In practice it is very difficult to distinguish between stochastic and chaotic non-linearity. It is also difficult to identify non-linear structures in time series when the hidden dynamics are complex. In this paper we provide evidence that in presence of specific high-dimensional underlying structures the White (1989) and Theiler et al. (1992) tests fail to detect non-linearity.

Seasonal Mackey-Glass-Garch Process and Short-Term Dynamics

The aim of this article is the study of complex structures which are behind the short-term predictability of stock returns series. In this regard, we employ a seasonal version of the Mackey-Glass-GARCH(p,q) model, initially proposed by Kyrtsou and Terraza (2003) and generalized by Kyrtsou (2005, 2006). It has either negligible or significant autocorrelations in the conditional mean, and a rich structure in the conditional variance. To reveal short or long memory components and non-linear structures in the French Stock Exchange (CAC40) returns series, we apply the test of Geweke and Porter-Hudak (1983), the Brock et al. (1996) and Dechert (1995) tests, the correlation-dimension method of Grassberger and Procaccia (1983), the Lyapunov exponents method of Gencay and Dechert (1992), and the Recurrence Quantification Analysis introduced by Webber and Zbilut (1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we forecast the return series using a seasonal Mackey-Glass-GARCH(1,1) model. The interest of the forecasting exercise is found in the inclusion of high-dimensional non-linearities in the mean equation of returns.

Analysing the Dynamics between U.S. Inflation and Dow Jones Index Using Non-Linear Methods

A growing body of literature concentrates on the linear dependence between stock returns and inflation. Although the recent empirical evidence suggested the presence of complexities, to our knowledge only a few works have investigated the existence of a potential nonlinear stock returns-inflation relationship. In order to study in more depth the dynamic attributes of this puzzle, we suggest a quite different framework where the primary goal is to explore the association between their underlying dynamics. Through the use of the Recurrence Quantification Analysis (Webber and Zbilut (1994)), the test for structural breaks of Bai and Perron (1998) and the test for nonlinear causality of Diks and Panchenko (2006), we find evidence in favour of negative nonlinear linkages between the inherent dynamics of inflation and stock returns. The presence of nonlinearity reinforces uncertainty. As long as inter-dependences are complex and nonlinear, small perturbations in fundamentals can lead to unexpected propagations within the financial system.

EXPLORING THE IMPACT OF CALENDAR EFFECTS ON THE DYNAMIC STRUCTURE AND FORECASTS OF FINANCIAL TIME SERIES

Several recently developed chaotic forecasting methods give better results than the random walk forecasts. However they do not take into account specific regularities of stock returns reported in empirical finance literature, such as the calendar effects. In this paper, we present a method for filtering the day-of-the-week and the holiday effect in a time series. Our main objective is twofold. On the one hand we study how the underlying dynamics of the Nasdaq Composite, and TSE 300 Composite returns series can be influenced by the presence of calendar effects. On the other hand we adapt our method to chaotic forecasting. Its computational advantages lead to significant improvements of forecasts.

Assessment of resampling methods for causality testing: A note on the US inflation behavior

Different resampling methods for the null hypothesis of no Granger causality are assessed in the setting of multivariate time series, taking into account that the driving-response coupling is conditioned on the other observed variables. As appropriate test statistic for this setting, the partial transfer entropy (PTE), an information and model-free measure, is used. Two resampling techniques, time-shifted surrogates and the stationary bootstrap, are combined with three independence settings (giving a total of six resampling methods), all approximating the null hypothesis of no Granger causality. In these three settings, the level of dependence is changed, while the conditioning variables remain intact. The empirical null distribution of the PTE, as the surrogate and bootstrapped time series become more independent, is examined along with the size and power of the respective tests. Additionally, we consider a seventh resampling method by contemporaneously resampling the driving and the response time series using the stationary bootstrap. Although this case does not comply with the no causality hypothesis, one can obtain an accurate sampling distribution for the mean of the test statistic since its value is zero under H0. Results indicate that as the resampling setting gets more independent, the test becomes more conservative. Finally, we conclude with a real application. More specifically, we investigate the causal links among the growth rates for the US CPI, money supply and crude oil. Based on the PTE and the seven resampling methods, we consistently find that changes in crude oil cause inflation conditioning on money supply in the post-1986 period. However this relationship cannot be explained on the basis of traditional cost-push mechanisms.

Nonlinear Features of Comovements Between Commodity Prices and Inflation

This paper attempts to investigate further the nonlinear feedback relationship found in Kyrtsou and Labys (2006) between US inflation (BLS CPI) and primary commodity price index (the BLS PPI component for all primary commodity series). Our goal is to disaggregate the above index to the individual commodity level for a group of raw materials prices, including crude oil. Assuming the hypothesis that a non-linear feedback relationship exists between US inflation and the commodity price index, we examine if individual primary commodity prices also nonlinearly causes inflation and vice-versa. We also improve upon our previous research by employing a new test for non-linear feedback causality recently developed by Hristu-Varsakelis and Kyrtsou (2006). Our results suggest the presence of non-linear interdependences between inflation and the various commodity price series, and particularly bi-directionality in the case of crude oil.