About Second Order Local Power of the Likelihood Ratio, Wald and Score Statistics in First Order Autoregressive and Moving Average Models

Abstract

In this paper we extend heuristically a simple formula for the local power of second order for the likelihood ratio, the Wald and score statistics, when a Gaussian autoregressive and moving average model of first order is considered and the interest and nuisance parameter vectors are multi-dimensional. The second order local power for the three criteria mentioned here are compared using particular models and hypotheses.