What can We Learn from Analysis of the Financial Time Series?

1. INVESTIGATION OF THE DISTRIBUTION AND SCALING OF FLUCTUATIONS FOR STOCK INDEX IN FINANCIAL MARKET In order to probe the extent of universality in the dynamics of complex behavior in financial markets and to provide a basic and appropriate framework for developing economic models of financial markets, we investigated the distribution of the fluctuations in the Hang Seng index — the most important financial index in the Hong Kong stock market [1]. The data include minute by minute records of the Hang Seng index from January 3, 1994 to May 28, 1997. It was observed that the distribution of returns in the Hang Seng index shows apparent scaling behavior, which cannot be modeled by a normal distribution. The non-Gaussian dynamics of the stochastic process underlying the time series of returns of the Hang Seng index, is better modeled by a truncated Lévy distribution which is shown in Fig. 1. A power-law behavior is observed for the probability of zero return for time intervals ∆t spanning at least two orders of magnitude. However, the power-law fall-off behavior in the tails deviate from that of Lévy stable process. The two tails of the distribution drop more slowly than a Gaussian, but faster than a Lévy process with an exponent outside the Lévy stable region. Especially after removing daily trading pattern from the data, the exponential deviation behavior from Lévy stable process is more clearly. The daily pattern thus affects strongly the analysis of the asymptotic behavior and scaling of fluctuation distributions. The exponential truncation ensures the existence of a finite second moment. The observations are useful for establishing dynamical models of the Hong Kong stock market [1].