Fuzzy clustering of time series with time-varying memory

Abstract

Little attention has been devoted to the long memory among the different data features considered for clustering time series. Following previous literature, we measure the long memory of a time series through the estimated Hurst exponent. However, we exploit the fact that a constant value for the Hurst exponent h is unrealistic in many practical examples. In this paper, assuming that the time series follows a multifractional Brownian motion, we estimate a time-varying Hurst exponent used as the input for a fuzzy clustering procedure. Motivated by the relevance of long memory in finance, the usefulness of the proposed clustering procedure is shown with an application to stock prices.