Near Observational Equivalence and Theoretical size Problems with Unit Root Tests

Jon Faust

59 citations0/0 files storedEconometric Theory

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Abstract

Said and Dickey (1984,Biometrika71, 599–608) and Phillips and Perron (1988,Biometrika75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

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References

1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1988Testing for a Unit Root in Time Series Regression 1984Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order 2010Critical Values for Cointegration Tests 1991Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots 1988Tests For Unit Roots: A Monte Carlo Investigation 1993Long-Run Economic Relationships: Readings in Cointegration.1991Critical Values for Cointegratio11 Tests*

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