Improvement in Hurst exponent estimation and its application to financial markets

Abstract

This research aims to improve the efficiency in estimating the Hurst exponent in financial time series. A new procedure is developed based on equality in distribution and is applicable to the estimation methods of the Hurst exponent. We show how to use this new procedure with three of the most popular algorithms (generalized Hurst exponet, total triangles area, and fractal dimension) in the literature. Findings show that this new approach improves the accuracy of the original methods, mainly for longer series. The second contribution of this study is that we show how to use this methodology to test whether the series is self-similar, constructing a confidence interval for the Hurst exponent for which the series satisfies this property. Finally, we present an empirical application of this new procedure to stocks of the S &P500 index. Similar to previous contributions, we consider this to be relevant to financial literature, as it helps to avoid inappropriate interpretations of market efficiency that can lead to erroneous decisions not only by market participants but also by policymakers.