Based On Empirical Likelihood Single-index Model Of Serial Correlation Test,

This paper mainly discussed about testing for serial correlation in single - index models. The V_Tp and Empirical Likelihood Statistics are constructed. The asymptotic distribution of those statistics under null hypothesis are shown. Through a numeric simulation, we get the behavior of those statistics under finite sample.Testing serial correlation in residuals for regression models is an important part in econometric data analysis. We say a model is good, if the residual (errors) of the model is independent and identified distributed, only by this assumption can we continue to estimate the parameters in the model, or do some hypothesis test on the model. Lacking of the i.i.d assumption will cause many problems. For example, the estimation of the parameters will not efficient; The significant test for variate will meaningless; And the forecast for the model is inefficient. The AR and MA models are commonly used among all the serial correlation models.Single - index model is one of the semiparameter models, which is more flexible than parameter models, easier to explain and more precise than nonparametric models. Single index models is important in econometrics and statistics. But the researchers has just set their first step on single - index models, the direction is still focused on the estimation for the parameter components and the nonparametric components. And the research on serial correlation test, or high rank serial correlation test, is still not done much.Empirical likelihood, proposed by Owen, is a nonparametric method of inference with sampling properties similar to those of bootstrap. The empirical likelihood ratio has a limiting chi-squared distribution, leading to hypothesis test and confidence interval. Compared with other classic statistic methods, empirical likelihood has many prominent merits. The empirical likelihood ratio confidence region is range preserving and transformation respecting, and the shape of the confidence region is determined mainly by data. And empirical likelihood confidence region need no information about variance matrix, which is hard to be estimated in statistics.One of the main results of the paper is to introduce empirical likelihood ratio to testing serial correlation in single - index models, and show the asymptotic distribution of the empirical likelihood ratio test statistics under null hypothesis, And we also extend the V_Tp test statistics into the single - index models, Then we investigate the properties of the two statistics under the finite sample through numeric simulation. Our methods are distribution - free, which overcomes the default of the score test, which depends on the error distribution.