Multiscale time irreversibility analysis of financial time series based on segmentation

Time irreversibility is a subject of increasing interest in an unbalanced system of various time series. Taking into account dynamic basic concepts, we provide multiscale time irreversibility analysis of financial time series based on segmentation which quantifies the time asymmetry in multiscales and is applied to several different forms of financial time series. Specifically, we adopt four distinct time irreversibility indices—Porta’s, Guzik’s and Ehler’s indices (P%, G% and E) and (gamma _{2,1} (k)), respectively, derived from data segments on various timescales. We investigate the performance of our statistical tests for local financial time series from segmented series system with known time reversal properties and find out that it can help classify the partially representative financial markets finally. Particularly, the smaller the scale factor L is the better the ability to distinguish data. Statistical analysis shows a close relationship between G% and E. On the contrary, the connection between P% and G% or P% and E is not proven. In addition, we define a new metric (gamma _{2,1} (k)) to measure the degree of time irreversibility. By further observing the results of the proposed method for computing the degree of irreversibility of the time series, we confirm that the asymmetry is an inherent property of the financial time series, which can be extended to a wide range of scales. Finally, we apply this method to the recurrence plot and multiscale recurrence quantification analysis, to compare effectiveness of the segmentation method.