On Hurst exponent estimation under heavy-tailed distributions

摘要: Abstract In this paper, we show how the sampling properties of Hurst exponent methods estimation change with presence heavy tails. We run extensive Monte Carlo simulations to find out rescaled range analysis ( R / S ), multifractal detrended fluctuation M F - D A detrending moving average ) and generalized approach G H E estimate on independent series different For purpose, generate random from stable distribution stability α changing 1.1 (heaviest tails) 2 (Gaussian normal distribution) using methods. prove be robust tails in underlying process. provides lowest variance bias comparison other regardless data sample size. Utilizing result, apply a novel intraday time-dependent high frequency for each trading day separately. obtain exponents S&P500 index period beginning year 1983 ending by November 2009 discuss surprising result which uncovers market’s behavior changed over long period.