The Establishment And Empirical Analysis Of GARCH Family Models Based On T-distribution

In financial markets,the characteristics of financial time series of returns are often characterized by "fluctuating aggregation","high-end thick tail" and "leverage effect",and these characteristics are often inconsistent with the assumption of normal distribution.In recent years,the distribution type of return on assets has been a hot research field for scholars.More and more types of distributions are proposed based on the normal distribution of returns.Among them,t-distribution has a certain advantage when it describes the distribution of “thick tail”.Compared with normal distribution,t-distribution can describe the characteristics of “thick tail” more than normal distribution.So the t-distribution can be closer to a true distribution with "thick-tailed" features.In this article,under the assumption of tdistribution,we can use the GARCH model to describe the characteristics of "highheavy tail","fluctuation-aggregation" and "leverage effect".And use the method of Maximum Likelihood Estimation to deduce the parameters of GARCH Model under the assumption of t-distribution.This paper applies the GARCH model proposed by western scholars in Chinese stock market to discuss whether the GARCH family models based on t-distribution can have a better applicability.Because Chinese specific national conditions and the perfection of financial markets are quite different from Western capitalist countries,so this study also has certain theoretical and practical significance.This article firstly introduces the classification and common distribution of returns in financial time series,then introduces the GARCH family models describing the volatility of returns,and derives the maximum likelihood estimation of the parameters of GARCH model based on t-distribution;Determine the GARCH(1,1)model as the final model and establish the GARCH(1,1)model under the assumption of the normal distribution,t-distribution,and generalized error distribution.Compare the parameter estimation results under the three distribution hypotheses,we could obtain that the GARCH(1,1)model has the best fitting effect under the assumption of t-distribution.In order to compare the prediction effect of the volatility,the volatility is predicted under the assumption that the residual item obeys the normal distribution and t-distribution.Finally,the GARCH(1,1)model established under the assumption of t-distribution is better for predicting the volatility of returns.