RESULTS ON ESTIMATION AND TESTING FOR A UNIT ROOT IN THE NONSTATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODEL

Sook Fwe Yap and Gregory C. Reinsel

Journal of Time Series Analysis, 1995, vol. 16, issue 3, 339-353

Abstract: Abstract. We review the limiting distribution theory for Gaussian estimation of the univariate autoregressive moving‐average (ARMA) model in the presence of a unit root in the autoregressive (AR) operator, and present the asymptotic distribution of the associated likelihood ratio (LR) test statistic for testing for a unit root in the ARMA model. The finite sample properties of the LR statistic as well as other unit root test procedures for the ARMA model are examined through a limited simulation study. We conclude that, for practical empirical work that relies on standard computations, the LR test procedure generally performs better than other standard procedures in the presence of a substantial moving‐average component in the ARMA model.

Date: 1995
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