The Correlation And Similarity Analysis Of Time Series

In recent years, the correlation and similarity analysis of time series have been extensively studied, ranging from economic fields, biological medicine, sociology and others. In the paper, we study some novel methods on the measurement of correlation and similarity, and apply them in the financial time series.First, the paper studies the q-dependent detrended cross-correlation coefficient. The new coefficient not only is able to quantify the strength of correlation but also allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. Besides, we get the pow-law exponents from the definition of q-dependent detrended cross-correlation coefficient, and verify that the exponent can indicate the correlation of cross-correlation scaling exponents and auto-correlation scaling exponents. By constructing two artificial time series:ARFIMA series and binomial multifractal series, we can conclude the strength of cross-correlations for different values of scaling parameters. Then we apply the method to analyze different stock time series, and find that the cross-correlation of S&P500 and DJIA is higher than that between SSE and DJIA. And for these three different time series, the correlation of cross-correlation scaling exponents and auto-correlation scaling exponents range differently for different parameters.Second, we propose a new method of similarity measurement:the reconstructed phase space information clustering method. The method is used to examine the similarity of different sequences by calculating the distances between them, which the main difference from information clustering method is the way to map the original time series to symbolic sequences. Here we make use of the state space reconstruction to construct the symbolic sequences not just taking account of the adjacent values of series and quantify the similarity of different time series considering the chaotic behavior between the complex time series. And we compare the results of similarity of artificial time series using the modified method, information categorization method and system clustering method. We conclude that the reconstructed phase space information clustering method is more effective to research the close relationship in time series and for short time series especially. Then we analyze the effect of various values of parameters on the results and applied the method to study the characters of stock time series from different areas and time periods.Finally, we construct the phylogenetic tree based on the pair-distances calculated by definition of correlation and similarity. The tree can reflect the clustering results and we conclude that the phylogenetic tree of stock time series can provide an effective suggestion for portfolio decision in the financial markets.