A Study of Longterm Memory in Stock Market Prices Using Rescaled Range Analysis

Abstract

Most of the studies on the behaviourof the Indian stock market using the autocorrelation function have revealed that the stock market is weakly efficient and the time series of stock prices and stock indices are random walks. The autocorrelation function assumes Gaussian or near-Gaussian properties in the underlying distribution. The distribution function is assumed to have the normal bellshaped curve. Mandelbrot [1972] has proved that the autocorrelation function works well in determining short-term dependence only. But it tends to underestimate long-run correlation for non-Gaussian series. Alternatively the Rescaled Range Analysis is used to study the long-term dependance in the time series. The Rescaled Range Analysis (R/S Analysis) is a nonparametric methodology developed by H. E. Hurst, a British hydrologist in 1951. Originally this methodology was applied to study the long-term storage capacity of reservoirs and later it was extended to study many natural systems. This statistical methodology is used for distinguishing random time series from biased random time series (Fractal time series) and to study the persistence of trends and also the presence of periodic and nonperiodic cycles in a time series. In this paper a study of the Indian stock market is carried out using the method of Rescaled Range Analysis and Hurst Coefficient. We conclude that the series of stock prices have persistent behaviour. Nearly 18% of the stock prices are influenced by the past. This ‘memory effect’ in the case of stock indices is found to be 23%. The stock market has shown persistent trends and that the series of prices and indices are biased random walks. The present prices are influenced by the past prices and this influence goes across time scales, one period influencing all the subsequent periods.