Michel Terraza

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.

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.

QUADRATIC PEN'S PARADE AND THE COMPUTATION OF THE GINI INDEX

Following Milanovics (1997) paper [Economics Letters, vol. 56, p. 45-49], we propose a simple way to compute the Gini index when income y is a quadratic function of its rank among n individuals.

Analyse des interdépendances non linéaires des principaux marchés boursiers de la zone euro

This paper analyzes the interdependencies of stock markets indices in the euro zone. We introduce an original dynamic model which is a combination of the noisy bivariate Mackey-Glass model of Kyrtsou and Labys [2006], extended in a multivariate framework, with DCC-GJR-GARCH errors. The empirical application conducted on seven market indices in the euro zone over the period from 11/28/2003 to 11/25/2012 highlights several mechanical interdependencies. The relationship detected in the mean equation confirm the leading role of the French and German indices, an organization of Southern Europe countries around the Italian index and the isolation of Greek and Irish indices. The psychological interdependencies revealed by the specification DCC-GJR-GARCH show two particular groups: the first is composed of ATHEX, CAC, ISEQ, IBEX and DAX indices and the second concerns the Italian and Portuguese indices. We find strong correlations for the Franco-German couple while we note a de-correlation, in the first group between CAC, DAX, ISEQ, IBEX with the Hellenic index following the sovereign debt crisis. The other indices are characterized by unstable psychological interdependencies on the study period.

Time-Frequency Analysis of the Relationship Between EUA and CER Carbon Markets

In this paper, interactions or co-movement between the CER and EUA futures prices are examined in order to shed light on the dependency between the European Union Emissions Trading Scheme (EU ETS) and the clean development mechanism (MDP). Our analysis uses the wavelet method to model the correlation between CER and EUA in the time-frequency domain. It highlights the impact of different investors (according to their investment horizons) on the co-movement between the CER and EUA prices, and therefore, the behavior of individual investors as speculators, arbitrageurs, and hedgers on European allowance and CDM credits cumulatively. In this vein, we analyze according to the frequency intervals, price convergence, identification of potential factors that could explain a difference in futures prices, and structural changes in the EUA and CER prices. The application is made using daily EUA’s and CER’s prices data.

Hedge Funds Risk-adjusted Performance Evaluation: A Fuzzy Set Theory-Based Approach

The hedge funds performance evaluation requires an adequate characterization of returns distributions shape. This characterization is made by thorough probabilistic moments. Different types of moments were used in the literature, namely, the conventional (central or raw) moments (Sharpe, 1966, Treynor and Black, 1973), the partial moments (Sortino and van der Meer, 1991, Sortino, van der Meer and Platinga, 1999, Bernardo and Ledoit, 2000, Sortino and Satchel, 2001, Farinelli and Tibiletti, 2008) and more recently the Trimmed L-moments (Darrolles et al., 2009). These authors generally define the performance ratio by dividing a location measure by a dispersion measure. The seminal approach deriving from the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), Mossin (1966) and Treynor (1962) uses the sample mean and the standard deviation of excess returns as location and dispersion measures respectively. These two statistics do not always adequately describe the returns distributions, especially in the presence of heavy tails and/or of skewness.

Hedge Funds Risk Measurement in the Presence of Persistence Phenomena

Measuring financial assets’ risks constitutes an essential tool for financial institutions to face up the future uncertainties. Thus, the VaR was designated by the Basel Committee as an instrument allowing daily estimation of the required funds to face up the market risks. Risks control is an important matter that animates not only professionals but also finance theorists. Indeed, at the academic level, the risk estimation represented by the parameter of volatility was the object of much research (see Diebold, 2005 for a review of literature). For the financial institutions, the risk constitutes a daily threat imperative for them to manage. Also, the control of this factor is a primordial objective, especially in a context of uncertainty. Thus, the last major crisis, known as the crisis of subprimes, has been an important systemic crisis with lasting consequences. Many authors wondered about the role of various financial assets in this crisis. Cartapanis and Teiletche (2008) concluded on the responsibility of hedge funds in one of the greatest economic crisis. Contrary to the preceding crises, which were limited to a particular sector, the crisis of subprimes was propagated to various sectors, and hedge funds are the main propagators.