Testing for unit roots in autoregressive-moving average models of unknown order

1984/01/01 by SAID E. SAID, Saïd E. Saïd, DAVID A. DICKEY +1 · 3,230 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Augmented Dickey–Fuller test #Autoregressive integrated moving average #Autoregressive model #Autoregressive–moving-average model #Cointegration #Econometrics #Financial Risk and Volatility Modeling #Mathematics #Monetary Policy and Economic Impact #Moving average #Moving-average model #SETAR #STAR model #Series (stratigraphy) #Statistic #Statistical hypothesis testing #Statistics #Test statistic #Time series #Unit root #Unit root test

paper · doi:10.1093/biomet/71.3.599

published in Biometrika 71(3), 599-607 (Oxford University Press)

openalex publication_date 1984/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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.

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