Local power of a Cramér–von Mises type test for parametric autoregressive models of order one

https://doi.org/10.1016/j.camwa.2008.01.022Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper, we study the local power of a Cramér–von Mises type test for parametric autoregressive models, when the data are stationary and ergodic. Our test is based on the limiting distribution of the cumulative residual process associated to the null model. We prove the contiguity of the null hypothesis H0 and a sequence of local alternatives that converges to H0 at rate 1/n from a fixed direction. From this result, the limiting distribution of the test statistic and the power are computed under these local alternatives. Simulation experiments show that the test is powerful against some exponential models.

Keywords

Conditional mean
Contiguity
Ergodicity
Goodness-of-fit
Martingale
Nonlinear models
Stationarity

Cited by (0)