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A sieve bootstrap for the test of a unit root. (English) Zbl 1036.62070
The authors consider a sieve bootstrap for a unit root test in models driven by general linear processes. Let the time series $$(y_{t})$$ be given by $$y_{t}=\alpha y_{t-1}+u_{t}$$ with $$(u_{t})$$ generated as $$u_{t}=\pi(L)\varepsilon_{t}$$, where $$L$$ is the usual lag operator and $$\pi(z)=\sum_{k=0}^{\infty}\pi_{k}z^{k}$$. The test of the unit root null hypothesis $$\alpha=1$$ is considered for $$(y_{t})$$ against the alternative of stationarity $$|\alpha|<1$$. The given model is first approximated by a finite autoregressive integrated process of order increasing with the sample size, and then the method of bootstrap is applied for the approximated autoregression to obtain the critical values for the usual unit root tests. The authors establish the bootstrap consistency of the tests and show that the bootstrap augmented Dickey-Fuller (ADF) tests are asymptotically valid. The finite sample performances of the bootstrap ADF tests are investigated and compared with the usual ADF tests through simulations.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F40 Bootstrap, jackknife and other resampling methods
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