Analysis of financial time series using discrete generalized past entropy based on oscillation-based grain exponent

Abstract

In this paper, we propose a new method, discrete generalized past entropy based on oscillation-based grain exponent (O-DGPE), which combines the discrete generalized past entropy and O-DGPE. It is proved to be a good measure of the uncertainty and reversed hazard rate of time series, and the oscillation information inside the data can be observed by this method. Firstly, we apply O-DGPE to chaotic maps. Experiments show that O-DGPE can distinguish different states of the map, and the results are also consistent with the actual nature of the maps. Chaos has higher uncertainty for inactivity time than periodic cycle. In addition, the law of O-DGPE changing with some parameters is also revealed. After that, we further validate the effectiveness of the method through ARFIMA model. Finally, we apply the method to financial time series. Results show that O-DGPE can be used to analyze stock markets from various perspectives. Through the character of O-DGPE changing with parameters, we can get a glimpse of the internal law of the financial markets. Chinese financial market is highly uncertain, while the stock exchange market of the USA is more mature. What’s more, the application of cumulative O-DGPE turns out to be very useful in measuring information on the inactivity time of a system.