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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

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