Study On The Wavelet And Frequency Domain Methods Of Financial Volatility Analysis

This dissertation studies the wavelet and frequency methods of financial volatility analysis. There are eight chapters in it. The main work and innovations are included in Chapter two to Chapter seven.In Chapter two, the frequency domain method of financial volatility analysis is studied. The estimation method of the dominating frequency of time series which are non-stationary and have long memory is proposed on the basis of the invertible short and long memory autoregressive integrated moving average model. A algorithm including the determination of the model orders of approximate maximum likelihood parameters estimation based on minimizing the sum of the squared residuals is put forward. The method is used to the return series analysis of China stock markets.In Chapter three, the time-scale method of financial volatility analysis is studied. Based on MODWT coefficients, a long memory analysis method using wavelet variance and a correlation analysis method using wavelet correlation and wavelet cross correlation for financial volatility are suggested. The methods are applied to the analysis of the properties of long memory and correlation of China stock markets volatility.In Chapter four, the properties of DWT coefficients of LMSV process are analyzed. For DWT coefficients of the same scale, correlation analysis and spectral analysis are taken separately. For DWT coefficients of different scales, correlation analysis is taken. The result suggests that for both the same scale and different scales, DWT coefficients of LMSV process are approximately uncorrelated.In Chapter five, the analysis method for structure change of LMSV model based on wavelet transformation is studied. According to the analysis results of DWT coefficients of LMSV process in the same scale, the method for detecting single structure change point using cumulative sums of squares of DWT coefficients and locating structure change point using MODWT coefficients is proposed as the DWT-CUSUMSQ-MODWT. The method for detecting and locating multiple structure change points of LMSV process is also put forward as DWT-ICUSUMSQ-MODWT. The methods suggested are proved to be effective and feasible by the structure change analysis of volatility of the return series of China stock markets.In Chapter six, the estimation method of LMSV model based on wavelet transformation is studied. On the approximate uncorrelation property of DWT coefficients of LMSV process in the same scale and different scales, first the quasi maximum likelihood estimation method of parameters and the estimation method of volatility process of LMSV model are presented. Then, the quasi maximum likelihood estimation method and the test method of long memory of volatility in LMSV model are proposed. The methods suggested are proved to be effective and feasible by the estimation of LMSV model of the return series of Shanghai stock market.In Chapter seven, the parameters estimation method of time varying LMSV model based on wavelet transformation is studied. In terms of the fact that wavelet transformation can decompose a process to different scales and on the approximate uncorrelation property of DWT coefficients of LMSV process in the same scale and different scales, the local likelihood function of time varying LMSV model is set up. Then, according to the relationship between DWT and MODWT coefficients, the local likelihood function of time varying LMSV model is represented in the form of parameters of the model and estimator of local wavelet variance. The method suggested is applied to the parameters estimation of time varying LMSV model of return series of China stock markets.The research is sponsored by National Natural Science Foundation of China: Persistence in Volatility of Multivariate Time Series and Its Application in Financial System(NO.70171001).