Study On Nonstationary Measure And Complex Measure Of Time Series

In this paper, we first discuss the complexity and nonstationarity of time series. Then, we study the method of measuring complexity and nonstationarity of time series based on the ergodic theory, coarse grain and information entropy. At last, the method is used to calculate and compare the complexity and nonstationarity of Shanghai Composite Index, Hang Seng Index returns, and others.This article makes the following research work:When measuring nonstationarity, we calculate the average sequence, the Lebesgue measure of stationary parts and the probability that the data comes into each stationary part. The method of measuring complexity is similar. We have improved the traditional methods. Based on the ergodic theory, we use the convergency value of convergent frequency sequences as the average value of the sequence in the stable interval. If the interval is unstable, the convergency value is meaningless. So, the concept of information structure should be given before calculating the complexity.Based on the above algorithms, we choose Shanghai Composite Index and Hang Seng Index returns as research subjects, and compare their nonstationarity and complexity with known data generating series of U(0,1) and N(0,1). The results verify the correctness of the algorithms.