Financial time series modeling using the Hurst exponent

• A method to detect long memory in the presence of structural breaks is proposed.
• Memory in absolute returns is found to increase when memory in actual returns grows.
• A model able to explain the memory in both absolute and actual returns is proposed.
• The new model outperforms the GARCH(1, 1) in terms of the Kolmogorov–Smirnov test.

This study aims to enhance the understanding of logarithmic asset returns. In particular, more emphasis is given to the long memory property of financial returns, a well documented stylized fact. However, in the presence of structural breaks other studies suggest that statistical tools such as the AutoCorrelation Function (ACF) can wrongly indicate long memory. We propose an insensitive to structural breaks method to test for dependence between distant observations. Furthermore, a model which combines memory in returns and memory in absolute returns is developed in two stages. First return series are segmented with respect to changes in the volatility and then the two parameters of the model are estimated. To assess the capabilities of the model, historical prices of the Standard and Poor 500 Index (S&&P500), Financial Time Stocks Exchange 100 Index (FTSE100), Deutsche Boerse Ag German Stock Index (DAX) and Crude Oil are used.1 Given the estimated parameters and the volatility within each regime, 10000 vectors are generated and compared to the original data in terms of the Kolmogorov–Smirnov (K–S) statistical test. The obtained results suggest that long memory is present and provide evidence that the additional memory information captured by the model improves financial returns modeling.