FTGARCH Model And GARCH-SVR Model For Forecasting The Volatility Of Financial Time Series

This paper mainly studies the volatility analysis and prediction in the field of financial time series.Firstly,I construct a functional threshold GARCH model under the background of high frequency time series,and give a model parameters estimation process.Secondly,I extend the NIC and CIRF under the discrete framework to the functional time series to analyze the characteristics of the functional GARCH model.Thirdly,I have absorbed the advantage of the semi-parametric method of the support vector machine,and combine it with the GARCH model to design the GARCH-SVR class method.Finally,the practical value of each model is tested in the actual financial market.This paper includes the following aspects:1.In the research of high frequency time series,threshold structure is introduced to con-struct functional threshold GARCH model on the basis of functional GARCH model.After determining the structure of the model,the stationarity conditions of the model are given.For the parameters to be estimated in the model,the functional principal component analysis method and parameter estimation method similar to the least squares method are used to estimate the pa-rameters.After describing the process of parameter estimation,I give a theoretical proof of the consistency condition of the estimated parameters.2.In order to characterize the asymmetry and cumulative effect of the volatility model of functional time series,I study the NIC and CIRF in the framework of discrete time series,and generalize them to functional form.On this basis,the NIC and CIRF calculation formulas of the functional GARCH model and the functional threshold GARCH model are derived.Then,we use the above tools to analyze the inheritance and extension of volatility characteristics from discrete time series to functional time series and from functional GARCH model to functional threshold GARCH model.3.In the research of low frequency time series,I introduce the GARCH-SVR model.The reason for choosing SVR model is that it can not only describe the non-linearity of data,but also transform the non-linearity of low-dimensional space into the linearity of high-dimensional space,which may be helpful to improve the efficiency of parameter estimation.In this way,we use the technology of parameter estimation and semi-parameter estimation to analyze the time series data.On this basis,the GJR model and the student t-distribution are used to analyze the asymmetry of volatility and the thick-tailed property of distribution respectively.4.Monte Carlo simulation experiments are carried out to test the parameters estimation and prediction effect of the above-mentioned volatility models.Compared with the function-al GARCH model,the simulation results show that the parameter estimates of the functional threshold GARCH model are closer to the real values of parameters to some extent,and the asymmetry of volatility can be judged by the parameters of the model.Compared with the ex-isting SVR-GARCH model and SVR-GJR model,the GARCH-SVR class model proposed by us have better performance in predicting volatility in most cases.5.I apply the functional threshold GARCH model to the stock market,and illustrate the rationality of the above model through practical examples.Then,the functional NIC curve and the functional CIRF are applied to the estimated functional GARCH model and the functional threshold GARCH model.It can be seen from the data analysis in the paper that this provides more comprehensive information for investors to the degree of asymmetry of data and models and the impact of current disturbances on future volatility.Finally,we apply the GARCH-SVR class models to market index and real exchange rate.The experimental results show the applicability of the proposed models.