Stochastic chaos or ARCH effects in stock series?: A comparative study

Recent empirical studies have shown that the chaotic behaviour and excess volatility of financial series are the result of interactions between heterogeneous investors. In our article, we propose verifying this hypothesis. Thus, we use the Chen et al. Testing for non-linear structure in an artificial financial market. Working Paper, University of Bonn (2000).] model to show that the modification of the agents' homogeneity hypothesis can drive to stochastic chaotic evolution of price series. Then, through an econometric procedure, we try to identify the underlying process of the Paris Stock Exchange returns series (CAC40). To this end, we apply several different tests: (1) dealing with long-memory components derives from the fractional integration test of Geweke and Porter-Hudak (GPH) J. Time Ser. Anal. 4 (1983) 221.] and (2) dealing with chaotic structures comes from the work on correlation dimension of Grassberger and Procaccia Physica 9D (1983) 189.] and the Lyapunov exponents method of Gençay and Dechert Physica D (1992) 142.]. Finally, we forecast the CAC40 returns series using the recent methods of Principal Components Regression (PCR) and Radial Basis Functions (RBF). We conclude with the implications of the presence of chaotic structures in stock markets and future research on ARCH and chaotic models' relationships.