Skewness, long-time memory, and non-stationarity: Application to leverage effect in financial time seriesH. E. Roman1, M. Porto2 and C. Dose3
1 Dipartimento di Fisica, Università di Milano-Bicocca - Piazza della Scienza 3, 20126 Milano, Italy, EU
2 Institut für Festkörperphysik, Technische Universität Darmstadt - Hochschulstr. 8, 64289 Darmstadt, Germany, EU
3 Hewlett-Packard - Via Giuseppe Di Vittorio 9, 20063 Cernusco sul Naviglio (MI), Italy, EU
received 4 July 2008; accepted in final form 3 September 2008; published October 2008
published online 26 September 2008
We analyze daily log-returns data for a set of 1200 stocks, taken from US stock markets, over a period of 2481 trading days (January 1996November 2005). We estimate the degree of non-stationarity in daily market volatility employing a polynomial fit, used as a detrending function. We find that the autocorrelation function of absolute detrended log-returns departs strongly from the corresponding original data autocorrelation function, while the observed leverage effect depends only weakly on trends. Such effect is shown to occur when both skewness and long-time memory are simultaneously present. A fractional derivative random walk model is discussed yielding a quantitative agreement with the empirical results.
89.65.Gh - Economics; econophysics, financial markets, business and management.
05.45.Tp - Time series analysis.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
© EPLA 2008