Estimation of the Hurst Exponent in Time Series of Daily Returns of Stock Indices

Abstract

One of the fundamental assumptions of the efficient market hypothesis and the modern portfolio theory are both Gaussian probability distribution and the independence of returns. This paper provides a brief historical review of efforts dealing with capital markets emphasizing their efficiency and counter-tendencies whose goal was to falsify the assumption of independence of returns and their normal distribution. This paper applies a measure of long-range dependence rediscovered and promoted by Mandelbrot to daily returns of 27 selected stock indices. This measure is called Hurst exponent and was estimated using rescaled range analysis. The results are in line with similar papers stating that the series of daily returns are prevailingly persistent which implies the presence of local trends. Such a finding falsifies the assumption of random walk in stock prices.