A new measurement of financial time irreversibility based on information measures method

In this paper, we propose a new measurement of time irreversibility based on information measures method to analyze the financial stock markets. In order to examine the effectiveness of this method, we employ it into ARFIMA models. Applying the new method to quantifying time irreversibility of 33 financial indices evolving over the period 2002-2016, we conclude that the stock daily prices of the companies are indeed time irreversible and the degree of irreversibility varies with time for each company. According to the values of irreversibility, we could rank the companies. Also we obtain that the values of annualized irreversibility may have little effect on the coefficient of variation. Moreover, in order to find patterns arising among different periods, we use the principal component analysis (PCA) and hierarchical clustering, the results obtained by these two standard techniques in data mining are in agreement.