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

TLDR

Recent methods for detecting unit roots in autoregressive and ARMA time series require specifying the number of AR and MA coefficients, and a unit root indicates non‑stationarity that can be remedied by differencing. This paper develops a test for unit roots based on approximating an ARMA model by an autoregression. The test statistic is the standard regression output, with a known limit distribution whose percentiles have been tabulated. An example illustrating the test is provided.

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.