Testing for a Unit Root in ARIMA Processes

Philip Shively

Journal of Applied Statistics, 2004, vol. 31, issue 7, 785-798

Abstract: A unit root has important long-run implications for many time series in economics and finance. This paper develops a unit-root test of an ARIMA(p-1, 1, q) with drift null process against a trend-stationary ARMA(p, q) alternative process, where the order of the time series is assumed known through previous statistical testing or relevant theory. This test uses a point-optimal test statistic, but it estimates the null and alternative variance-covariance matrices that are used in the test statistic. Consequently, this test approximates a point-optimal test. Simulations show that its small-sample size is close to the nominal test level for a variety of unit-root processes, that it has a robust power curve against a variety of stationary alternatives, that its combined small-sample size and power properties are highly competitive with previous unit-root tests, and that it is robust to conditional heteroskedasticity. An application to post-Second World War real per capita gross domestic product is provided.

Keywords: Point-optimal; Invariant; Unit Root; ARIMA; Gross Domestic Product (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1080/0266476042000214547

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