Multiscale Time Irreversibility Analysis Of Time Series And Its Application In Financial Markets

Time irreversibility is one of important properties of non-stationary time series. Complex time series often demonstrate multiscale time irreversibility, such that not only the original but also coarse-grained time series are asymmetric over a wide range of scales. Firstly, we study the multiscale time irreversibility of time series. In this paper, we put forward a method based on statistical moments, which is called multiscale multifractal time irreversibility analysis (MMRA). In order to verify its effectiveness, we utilize multiscale time irreversibility analysis (MSRA) and multiple testing strategy of temporal irreversibility (MBRA) as comparision.Secondly, we employ three methods into the time irreversibility study of three time series. Two of them are artificial time series:one is based on the delayed Henon map, another one is generated from the binomial multifractal model. It turns out that MMRA detects and depicts time irreversibility and multifractality of two series in a nice way. MSRA describes the irreversibility of time series with different values of parameters, while MBRA reflects the irreversibility of time series directly. Another type of time series that we study is financial time series. Though MMRA method, we find that mul-tiscale time irreversibility has a close link with the evolution stage of stock markets, the generalized Hurst exponent and multiscale time irreversibility of emerging market are larger than those of developed markets. MSRA has also proved that the exchange energy flow of Asia stock markets is larger than those of other markets. MBRA has de-picted the time irreversibility of Asia stock markets in the skewness angle. MMRA has provided different study angles in assessing evolution stages of stock markets, which has a certain application prospects.Last but not the least, we introduce multifractal detrended fluctuation analysis (MF-DFA) and apply it into artificial time series and financial time series. Then we compare the generalized Hurst exponent from MMRA and MF-DFA. The two generalized Hurst exponents have their own advantages and features, which characterize the multifractal-ity degree of time series from different ways.