TESTING THE ORDER OF DIFFERENCING IN TIME SERIES REGRESSION

Abstract. In this paper we develop a test procedure for detecting overdifferencing or a moving-average unit root in time series regression models with Gaussian autoregressive moving-average errors. In addition to an intercept term the regressors consist of stable or asymptotically stationary variables and non-stationary trending variables generated by an integrated process of order 1. The test of the paper is based on the theory of locally best invariant unbiased tests. Its limiting distribution is derived under the null hypothesis and found to be non-standard but free of unknown nuisance parameters. Asymptotic critical values, which depend on the number of integrated regressors, are obtained by simulation. A limited simulation study is carried out to illustrate the finite sample properties of the test.