Permutation transition entropy: Measuring the dynamical complexity of financial time series

Abstract

Abstract In this paper, we propose a new approach to measure the dynamical complexity of a single time series. We characterize the changes of the states of the underlying system, by quantifying the Markov states transition between adjacent permutations. Unlike many static-complexity measures, the new method of permutation transition entropy (PTE) is able to identify the dynamical complexity with respect to the change of the temporal structure. With the numerical analyses, we show that the PTE can give the information that other methods, like the permutation entropy (PE), cannot. We apply the PTE method to the financial time series analysis, which reveals the existence of the momentum effect in the daily closing price and the daily trading volume of Chinese stock markets. It indicates that the dynamical complexity of these two indexes in stock markets is lower than that of the random time series. While the logarithm return and the logarithm change of trading volume show very similar PTE values with those of the random time series, which represents higher randomness.