TTA, a new approach to estimate Hurst exponent with less estimation error and computational time

Abstract

Investigation of long memory processes in signals can give us an important information about how signals have behaved so far and how will it behave in future. Hurst exponent estimation is a proper tool to show memory in signals. Rescaled range analysis (R/S), detrended fluctuation analysis (DFA) and generalized Hurst exponent (GHE) are most known methods for estimation of Hurst exponent which introduced in literature. In this paper, we propose a new algorithm to estimate Hurst exponent based on triangles total areas (TTA) that can be made out of three samples of different lag in time series. To test our algorithm performance, we used two kinds of synthetic waveforms with known Hurst exponents. Results indicates that the proposed method is superior with respect to data length, estimation error, computational time and noise sensitivity. We also apply our proposed method in epilepsy detection and compare our results with previous works to show outperformance of our algorithm with accuracy of 94.5% in classification between interictal and ictal EEG signals.