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On the theory of testing for unit roots in observed time series. (English) Zbl 0602.62074
The paper presents some new most powerful invariant tests for the unit root null hypothesis against the one-sided non-stationary (non-explosive or explosive) alternative hypothesis, for the errors of a linear regression model. The test statistics proposed is applied to the problem of testing the random walk and the random walk with a constant drift null hypotheses against stationary and non-stationary one-sided alternatives. The test statistic corresponding to each case mentioned above is simplified to a form which can be viewed as a von Neumann type ratio, and the exact significance levels are tabulated. The paper ends with two interesting numerical applications to real-life data.
Reviewer: P.Stoica

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B84 Economic time series analysis
60G50 Sums of independent random variables; random walks
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