Seasonal Moving‐average Unit Root Tests in the Presence of a Linear Trend

Wing‐kuen Tam and Gregory Reinsel

Journal of Time Series Analysis, 1998, vol. 19, issue 5, 609-625

Abstract: To distinguish stochastic from deterministic seasonality, test procedures are developed for a unit root in the integrated seasonal moving‐average (SMA) model when an underlying deterministic trend is present. Locally best invariant unbiase (LBIU) and point optimal invariant tests are considered. Their asymptotic distributions are developed and are found to differ from those for the no‐linear‐trend case. The limiting distribution of the LBIU statistic is expressed as a functional of Brownian motions. The procedures are extended to more general seasonal autoregressive moving‐average (ARMA) models, and to the inclusion of exogenous regressors. Finite‐sample distributions are also derived for the SMA(1) model. Simulations suggest that these distributions provide accurate approximations for more general ARMA models. A numerical example is included to illustrate the tests.

Date: 1998
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