Sequential empirical process in autoregressive models with measurement errors

Abstract

In this paper, we study the weak convergence of the sequential empirical process based on the residuals from autoregressive models with measurement errors. It is shown that the sequential empirical process converges weakly to the sum of a Gaussian process which is the limit of a sequential empirical process of certain p-dependent random variables and an additional term depending on the parameter estimators of the model. As an application, we discuss the change point problem in the distribution of the error process in the autoregressive model. We present the numerical result of a simulation study for an asymptotically distribution-free test.