The Statistic Research And Empirical Analysis Based On Value At Risk (VaR)model And Back-test

The core of economy is finance, the risk of which is directly related to people’s vital interest. Taken statistical techniques as the primary method, Value at risk(Va R) model is the main model to depict risks of financial time series and has been highly concerned for its simplicity.Under the relevant background of value at risk, this paper, at first, briefly introduces the background of value at risk as well as the main research achievements made by scholars in this field in recent years, and then demonstrates the common constant variance of time series model and heteroscedasticity of time series model.In view of respective advantages of the ARMA model depicting constant variance and the EGARCH model depicting heteroscedasticity, the ARMA model is combined with the EGARCH model into the ARMA-EGARCH model to study the financial time series.Then, this paper introduces related definition of Va R and several models to estimate the value of Va R. Considering that both the extreme value theory and Va R model study the extremum problem of distribution, this paper presents the extreme value theory and the ARMA-EGARCH-GDP model which combines the extreme value theory with the ARMA-EGARCH model. What’s more, in consideration of the historical simulation model which can avoid to make any assumption on the distribution of time series, this paper proposes the ARMA-EGARCH- semiparametric model combining the ARMA-EGARCH model with the historical simulation method to estimate the Va R.It’s shown by the definition of Va R that the calculated Va R value is an estimate no matter how good the Va R model is in theory. So, it is necessary to test the accuracy of these estimates. This paper, therefore, introduces a common method of testing the accuracy of Va R-----the likelihood ratio test. Meanwhile, the likelihood ratio test evaluates pros and cons of a model on the whole. It cannot reject models that failure occurs successively in a certain period of time and that no failure occurs successively in another certain period of time. So, regarding this problem, the paper proposes T test to test the accuracy of Va R and introduces its relevant theory.In the end, this paper analyzes empirically the ARMA-GARCH-GDP model and the ARMA-EGARCH-semiparametric model by the Shanghai composite index under the confidence level of 99%, 95%, 90% respectively, and makes back-test on the two models’ Va R by the traditional Kupic likelihood ratio test and the T test. The empirical analysis result is as follow: Likelihood ratio test accepts the ARMA-EGARCHsemiparametric model and the ARMA-EGARCH-GDP model under those three kinds of confidence level. But the T test only accepts these two models under the confidence level of 95% and 90% and rejects the ARMA-EGARCH-semiparametric model and the ARMA-EGARCH-GDP under the confidence level of 99%.The empirical analysis result shows that the ARMA-EGARCH-semiparametric model can be used as a model to estimate the value of Va R and that the accuracy of models accepted by T test is higher than that of models accepted by likelihood ratio test under the high confidence levels.