Financial Volatility Model Based On Moments Of Time Series

Accompanied by financial risk all time, financial market has made great progress. It is common problem on how to measure the change and character of financial risk and how to avoide the risk in terms of theory and practice. In the past time, variance risk of financial volatility, which is described by the second moments, has been discussed. Lots of achievements have been obtained in the research. However, higher moments risk has not been pay more attention to. To describe the time-varying and persistence character of higher moments'risk, the dissertation will discuss the modeling of higher moments. The main work and innovations of the dissertation include:1. NAGARCHSK-M model and its modeling technic are put forward and discussed in detail. Then, three forms of multivariate GARCHSK model are put forward and compared. Based on Gram-Charlier expansion of normal distribution, we provide the method for estimating parameters in multivariate GARCHSK model. At the same time, multivariate volatilities of conditional higher moments are estimated through IC-GARCHSK model, which is depended on Independent Component Analysis.2. In the volatility modeling for the second moments, the properties of SR-SARV model and its parameter estimating are discussed, which is completed by Kalman filters. As for Box-Cox-SV model, the character of the model's moments and auto-correlation about squared series is demonstrated.3. We make full use of the approach of impulse response analysis in the research. On the one hand, the definition of volatility persistence and common persistence of higher moments'series is established, and the theorem of volatility persistence and common persistence is proved, which shed the light on finding vector of common persistence. On the other hand, the conception of fractal cointegration and fractal common persistence is put forward, which extends the research about volatility persistence and common persistence in the frame of integer dimension.4. Wavelet analysis is leaded into the process of modeling in the dissertation. Based on wavelet multiresolution analysis, multiresolution cointegration and error correction model is established, and further its modeling method is discussed. The new conception of multiresolution persistence and multiresolution common persistence and its modeling methods are also put forward. In the empirical study,multiresolution portfolio and multiresolution CAPM model are obtained to suit to multiresolution risk.5. Modeling method of multiresolution nonlinear cointegration is discussed on the basis of wavelet neural network. In addition, nonlinear common persistence in higher moments'series is also discussed. The empirical results reveal that the variance process and skewness process have the same vector of nonlinear common persistence, which imply that there exist a nonlinear combination will not only reduce persistence in variance process, but also reduce persistence in skewness process.6. To deal with higher moments'risk, dynamic portfolio tactic and CAPM model are inferred in the dissertation based on Taylor expansion of utility function. Good empirical results are achieved in the end.The research is sponsored by National Natural Science Foundation of China: Research on Long Run Eqilibrium in Multivariate Moments Series and Avoiding Tactics of Dynamic Financial Risk (No. 70471050).