Non-parametric Regression Models And Serial Correlation Test And Heteroskedasticity Test

Testing serial correlation and heteroskedasticity in econometric models for regression models play prominent roles in econometric data analysis. We generally assume that the errorsε_i are mutually independent and homoskedastic in regression models. If theε_i are not independent, i.e. E(ε_iε_j)≠0,i≠j, we say that the models are serially correlated. If the error variances are not equal, i.e. Var(ε_i)=σ_i~2,i=1,..., n, we say that the models are heteroskedastic. We request the fitted residuals are white noise for a good fitted models, that is to say the residuals don't include any information of the models. So the assumptions of independent and homoskedasticity are some basic assumptions. Under those assumptions, we can do some ordinary statistic inference such as parameter estimate, hypothesis test and further to forecast.Empirical likelihood, proposed by Ower,(1988, 1990), is a nonparametric method of inference. Compared with other classic or modem statistic methods, empirical likelihood has many prominent merits. For example, the empirical likelihood ratio confidence region is range preserving and transformation respecting, and the shape and orientation of the resulting confidence regions are determined entirely by the data.One of the main results of the paper is firstly introduced empirical likelihood ratio test to test serial correlation and heteroskedasticity in nonparametric regression models, and we derived the nonparametric version of Wilk's theorem of empirical likelihood. The second result is that we extend the method of Li & Hsiao(1998) to test serial correlation nonparametric regression models.