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Testing for unit roots in autoregressive-moving average models of unknown order. (English) Zbl 0564.62075
Given a sample from a process \(\{Y_ t\}\) that follows an ARMA model with unknown order, the presence of a unit root in the autoregressive operator is tested. The suggested procedure uses an autoregressive approximation, and leads to regress \(\dot Y_ t=Y_ t-Y_{t-1}\) on \(Y_{t-1}-\bar Y\), \(\dot Y_{t-1}\), \(\dot Y_{t-2},...,\dot Y_{t- k}\); suggestions about how to deal with the choice of k are given. Then the studentized statistic \({\hat \tau}\) is computed, which is the estimated coefficient of \(Y_{t-1}-\bar Y\) divided by its estimated standard deviation. The limiting distribution of this statistic is that of \(\tau_{\mu}\) listed in W. A. Fuller, Introduction to statistical time series. (1976; Zbl 0353.62050), p. 373. Mathematical derivations and a numerical example are provided.
Reviewer: R.Mentz

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
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