A Nonlinear Correlation Analysis Of Financial Time Series Based On Wavelet Analysis

The correlation analysis is very important in financial analysis. The linear correlation and Granger causality analysis methods are used in the correlation analysis method widely, but they all have certain limitation in financial markets. Some data is often heavy tail distribution, their variance sometimes does not exist. Linear correlation between variables can not capture the nonlinear relation, and when use it to analyze the correlation between variables which have nonlinear relation between each other can lead to misunderstanding, therefore, we cannot use linear correlation coefficient to reflect non linear correlation. Wavelet method could separate high frequency part and low frequency part of the data isolated, high-frequency partly reflect short-term trend of the financial market, while the low frequency part reflects the mid-term or long-term financial market trends. Therefore, by wavelet analysis method, people can understand the variation in the market more synchronous. And in the research on Copula method also rise more convenient on correlation analysis(especially tail correlation). This article will introduce the wavelet analysis to the nonlinear correlation research of financial time series, combining Copula technology, focusing on the correlation between the two countries to do a comprehensive and in-depth discussion. First, it introduced Copula function in detail, and pointed out the superiority of its application. Then he correlation of stock market in China and U.S.A will be studied in this paper with multi-resolution analysis. The data is decomposed into two parts-approximate part and detail part. Then Pearson dependence coefficient and rank dependence coefficient between the data of each level are estimated to explain the correlation of stock markets between China and U.S.A. At last, multi-resolution analysis and Copula method are combined together to analyze the correlation of stock markets between China and U.S.A. Meanwhile, including Pearson r, Kendallτ, Spearmanρand tail dependence. The taildependence analysis of each decomposed level of index return with Gumbel copula and Clayton copula makes the most kernel part of this paper, and the quantified correlation dependence could forecast the change in stock market in the future.