Time series clustering based on time-varying Hurst exponent

We consider the problem of clustering time series which are assumed to possess the long term memory. We propose an approach based on combining the results obtained by applying different methods for estimating time-varying Hurst exponent and apply it to Euro exchange rates. Firstly, we fit AR-GARCH models to every time series to reduce bias of rescaled range analysis method. We only consider model with residuals, in which no autocorrelation and ARCH effect is present; among them we choose the model with the lowest value of the Bayesian information criterion. Afterwards, we estimate the Hurst exponent from the residuals by means of the rolling window approach using four different estimation methods. Vectors of Hurst exponents are clustered for each of the four cases and the clusters are compared in order to obtain the final clustering.