The Selection Of Conditional Heteroscedastic Model Via Density Forecasts

An important research direction is the use of econometric methods, such as financial time series analysis. Among them, the fat tail and Leptokurtic with volatility clustering phenomenon of the return series show great significance for financial practices. A lot of conditional heteroskedastic models for volatility have being putted forward by the scholars.The evaluations of these models always focus on the description and pre-diction accuracy of the model for the particular characteristics of financial data, and not about the model fitting accuracy of the data. This article will use a new method to evaluate the fitting accuracy of the two types of models. Didbold’s density forecasts method provides a tool to answer this question.Density forecasts base on the conditional probability density function pro-vided by the model, able to model fit and predictive ability evaluation. The method can assess the performance of different models that not contain, and can be easily extended to the multi-step density forecasts and multivariate density forecasts flexibly.Didbold use the histogram and sequence diagram instead of the tradi-tional tests for the independent uniformly distribution, but there some certain limitations. This paper, the method of the supplement in the amount of data is small, the Greenwood statistic is used to instead of the histogram method. On this basis, a preliminary discussion on the method is taken.Meanwhile, we use five different models in the Shanghai Composite Index daily closing price, with the error term distribution model based on the stan- dard normal distribution and students t-distribution,and take a comprehensive analysis and evaluation on the five different models.