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Biometrika 1984 71(3):599-607; doi:10.1093/biomet/71.3.599
© 1984 by Biometrika Trust
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Testing for unit roots in autoregressive-moving average models of unknown order

SAID E. SAID and DAVID A. DICKEY

Department of Mathematics, East Carolina University, Greenville, North Carolina, U.S.A.
Department of Statistics, North Carolina State University, Raleigh, North Carolina, U.S.A.

Recently, methods for detecting unit roots in autoregressive and autoregressive-moving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an autoregressive-moving average model by an autoregression. The test statistic is standard output from most regression programs and has a limit distribution whose percentiles have been tabulated. An example is provided.

Key Words: Mixed model • Nonstationary • Time series • Unit root


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