Testing for unit roots in autoregressive moving average models: An instrumental variable approach

Abstract In this paper we propose an approach, based on an instrumental variable estimator, for testing the null hypothesis that a process Y t is an ARIMA( p , 1, q ) against the alternative that it is a stationary ARIMA( p + 1, 0, q ) process. Our approach is an extension of the procedure suggested by Hall (1989a) for the case p = 0. We derive the limiting distributions of the instrumental variable estimator when the estimated model is either (i) the true model, (ii) the true model with a shift in mean included, or (iii) the true model with a shift in mean and a linear time trend included. The performance of the test statistics is investigated using a Monte Carlo study. Generally speaking, the criteria based on the instrumental variable approach seem to perform as good as or better than the existing methods when the model is specified correctly. However, if the model is overspecified, then the empirical levels are higher than the nominal level in moderate-sized samples, whereas if the model is underspecified the instrumental variable estimators are inconsistent.

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