Testing Hereoscedasticity In Varying-coefficient Models

Testing serial correlation and heteroscedasticity in residuals (errors) for regression models are important practice in econometric data analysis. We generally assume that the errorsεi ,sare mutually independent and homoscedastic in regression models. If theεi ,s are not independent, i.e. Eεiεj≠0, i≠j, we say that the models are serially correlated. If the error variances are not equal, i . e. ( )Varεi =σi2 , i = 1, ,n, we say that the models are heteroscedastic. 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 homoscedasticity are some basic assumptions. Under those assumptions, we can do some ordinary statistic inference such as parameter estimate, hypothesis test and further to forecast. Violating those assumptions can lead to many problems. So, it's necessary to diagnose heteroscedasticity and serial correlation before statistic inference.Varying-coefficient model is one of very important statistical models, which is developed in recent years, containing many special models. Since its birth, the scholars pay more attention to it, and have a lot of researches. However, previous literature focuses on the estimation of the varying-coefficient models, and testing of the heteroscedasticity of the model is less involved. As mentioned earlier, if heteroscedasticity exists, we may meet many problems in the practice, and have serious consequences. We mainly discuss the statistical diagnose in this paper.One of the main results of the paper is firstly introduced score test to test heteroscedasticity in varying-coefficient model, We get the asymptotic distribution of the score test statistics under the null hypothesis. We also investigate the finite sample properties of our statistics. The second result is that we research the heteroscedasticity of the partial varying-coefficient model based on the empirical likelihood method. We get good effect through numerical simulation.