An econophysics approach to the Portuguese Stock Index—PSI-20

Abstract

We analyse the PSI-20 (Portuguese Stock Index) data series from 1993 to 2001, with a view to examining the structure of the series, the appropriateness of the standard model forms for these data and evidence for market maturation. The data demonstrate several distinct behavioural periods, with characteristic dependence on different time-scales, and increased volatility during 1998–2000. The distribution of the daily logarithmic variation reveals an exponential decay in the central region, with typically fatter tails than expected from the Normal distribution. In particular, the characterisation of the time series profile of the daily variation with respect to the index value shows a power-law with exponent 1.58 different from those predicted by the additive and multiplicative models. In addition, we model the index series using a fractional Brownian motion formulation to obtain the Hurst exponents evaluating these through detrended fluctuation analysis, with different window sizes. It seems clear that persistence is a feature of the initial period, but is not evident (as might be expected) for periods of high volatility. However, some indication of recent improvements in stability is observed even for coarse-graining. This transition from persistent to anti-persistent behaviour is clearly reflected in the Hurst exponent values and supports to some extent the notion of volatility clustering. Furthermore, the grouping of similar exponent values as the series data evolve suggests that short-term memory is exhibited by the original series, even when volatility is relatively high. These findings are broadly supported by a further analysis of persistence in trends for the returns series, with the autocorrelation function for the returns, η t = δX t / X t , of the PSI-20 indicative of stronger short-term memory effects, although the modulus of return is not autocorrelated.