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 (1996) and Cordeiro et al. (1998). 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.

Key words: ARMA models; Bartlett-type correction;
chi-square distribution; score statistics; monotone correction; time series.

Kakizawa, Y. (1996) Higher
order monotone Bartlett-type adjustment for some multivariate test statistics.
Biometrika, 83, 4, 923-927.

Cordeiro, G. M., Ferrari S.L.P. and Cysneiros A.H.M.A. (1998) A
formula to improve score test statistics. Journal of
Statistical Computation and Simulation, 62, 123-136.