Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods

Abstract

Quasi-likelihood ratio tests for autoregressive moving-average (ARMA) models are examined. The ARMA models are stationary and invertible with white-noise terms that are not restricted to be normally distributed. The white-noise terms are instead subject to the weaker assumption that they are independently and identically distributed with an unspecified distribution. Bootstrap methods are used to improve control of the finite sample significance levels. The bootstrap is used in two ways: first, to approximate a Bartlett-type correction; and second, to estimate the p-value of the observed test statistic. Some simulation evidence is provided. The bootstrap p-value test emerges as the best performer in terms of controlling significance levels. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

A note on Bartlett correction factor for tests on cointegrating relations

“…By using the empirical distribution function in place of some specific parametric distribution, the non-parametric bootstrap does not require a choice of the error distribution, and this feature may be appealing to the applied researcher. Canepa and Godfrey (2007) propose computing the Bartlett adjustment for a quasi-LR test using non-parametric bootstrapping as a simple method to generate a non-normality robust small sample inference procedure in the context of ARMA models. An alternative procedure is a straightforward application of the bootstrap p-value approach.…”