Wavelet-based Frequency Domain Analysis Of Financial Data

Time and frequency are two of the most important characteristics to portray the signal. Time series analysis is the most typical methods on research on time-domain. According to the system that limited the length of the observational data, one can establish more accurately mathematical model that can reflect the time series contained in the dynamic dependencies, and predict the future behavior of the system. Time domain has been very deeply studied, and combined with many other theories such as chaos theory, the formation of a chaotic economic time series. Researches in the frequency domain have set Fourier analysis as the foundation contents. Recently, wavelet analysis theory became very popular and was the most ideal in this area. This article is based on wavelet analysis theory and depicts the instantaneous frequency of the signal, and for the analysis of the Shanghai Composite Index, the article find out the general law of the frequency of changes. The main work can be summarized as follows:With the help of wavelet analysis theory, this article studies the financial series from the view of frequency domain analysis, and use wavelet ridge to characterize the instantaneous frequency. Besides, it discusses the selection of mother wavelet function and the problem of boundary extension processing. Compared with the general research methods this article chooses special approach. After removes the trend of Shanghai Conposite Index in the past few years, the article depicts the variation of the residual fluctuations in the frequency.And then use the power spectrum analysis of wavelet transform, by changing the scale to detect the volatility of Shanghai Composite Index that in the past few years the index is mainly concentrated in the vicinity of two frequency components. Also analyze the rate of return of the index by the same power spectrum analysis. Finally, based on the abrupt changes of the stock index in the time domain and the power spectrum analysis the passage reveals an indicator which can monitor the abrupt changes in the stock market.