Some corrections of the score test statistic for Gaussian ARMA models

Abstract

In this article we compute three corrected score statistic versions: the Bartlett-type correction and the monotone corrected score statistics proposed by Kakizawa [Biometrika 83 (1996) 923–927] and Cordeiro, Ferrari and Cysneiros [J. Stat. Comput. Simul. 62 (1998) 123–136]. These corrected statistics are used to test the null hypothesis concerning some parameter of interest of an ARMA model, assumed to be Gaussian, stationary and invertible. We also consider the situations where nuisance parameters are present. The formulas are written in matrix form, appropriate for the use of symbolic or numerical languages. Some simulation results are also presented for the AR(1), MA(1) and ARMA(1, 1) models.