Diagnostic Analysis For Nonlinear Model With AR(p) Errors And Autoregression

This paper consider estimation and hypothesis test for nonlinear re-gression models with AR(p) error and autoregressive structure. Non-linear regression models with AR(p) error and autoregressive structure, which is important in practice, is an extension of linear regression mod-els with AR(1) errors.The main contributions of this paper is to apply the method of score test to study the simultaneous test of heteroscedasticity and autocorre-lation, the test of heteroscedasticity with autocorrelation and the test of autocorrelation with homoscedasticity for nonlinear regression mod-els with AR(p) error and autoregressive structure and obtain the corre-sponding test statistics; Furthermore, asymptotic distributions of all test statistics are discussed; Simulations are conducted to confirm the effec-tiveness of our methods.This paper consist of the following sections:In the first chapter, we introduced the research background, the im-portance and the research progress about nonlinear models.In the second chapter, the model of this paper and some related basic knowledge were introduced.In the third chapter, the score function and Fisher information matrix for the model of this paper were obtained.In the forth chapter, we presented the score simultaneous test statis- tics of heteroscedasticity and autocorrelation, the score test statistics of heteroscedasticity with autocorrelation and the score test statistics of au-tocorrelation with homoscedasticity; The asymptotic distributions of all score test statistics are also discussed.In the fifth chapter, Monte Carlo methods were conducted to study the properties of the score statistics for moderate sample sizes.In the sixth chapter, we summarized this paper and discussed the further research which can be carried out in future.