Detekce změn v časových řadách

Abstract

In the present work we study di®erent methods for testing whether or not a change has occurred in the parameter values of an autoregressive model (AR). We discuss the changes in the mean and in the autoregressive coe±cients of this model and also the changes in the variance of the white noise. This work presents two approaches to this problem. The rst one is based on the Gaussian likelihood ratio and the second one is based on asymptotical behavior of the score statistics derived from likelihood function. Further, we consider the generalized integer nonnegative autoregressive model (GINAR) dened by Steutel and van Harn random operator which can be written as an AR process under some conditions. Finally we study the signicancy and the power of these tests to detect the change point in the AR processes and their application to the GINAR processes despite the violation of some assumptions.