Testing Serial Correlation In Additive Model

Additive model is an important nonparametric model. It is usually applied into economicstatistics and analysis of financial time series. Additive model can not only fit linear data, butalso fit nonlinear data. Furthermore, it can effectively avoid the “curse of dimensionality”problem in ordinary nonparametric regression model. As a result, it is significant to studyadditive model.At present, there are many specialist have researched the estimate methods and theirasymptotic properties of additive model. However, testing serial correlation in this model hasbeen studied infrequently. We generally request the fitted residuals are white noise for a goodfitted model, namely the residuals meet the assumptions of independent and homoscedasticity.If the assumption of independent has destroyed, the model is serially correlated, and that willlead to many problems, such as that estimator is invalid, forecast is failure etc. This thesis isprecisely based on this consideration, and the test for serial correlation has been investigatedin additive model. The main contents of this paper are arranged as follows:The first chapter is the introduction part. We mainly introduce tests for serial correlationand the status of additive model as well as empirical likelihood method.In the second chapter, we study the estimation of additive model and their asymptoticproperties. This lays the foundation for testing serial correlation of additive model and theproof of relative theorems.In the third chapter, we propose the test methods of usingV_T,Pand empirical likelihoodratio to test serial correlation in additive model.V_T,Ptest statistics and empirical likelihoodratio test statistics are structured. Then their asymptotic distributions under null hypothesis arederived separately. The simulation and example analysis are implemented. And the resultsshow that both the tests are perfect at finite sample properties.The theorems and conclusions of Chapter3are proved in the fourth chapter.The fifth chapter is a summary of the full text, and what’s more, it has made a prospect offurther study.