UNIT ROOT TESTS WITH INFINITE VARIANCE ERRORS

Sung K. Ahn · S. Fotopoulos · Lijian He

22 citations0/0 files storedEconometric Reviews

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Monetary Policy and Economic Impact Complex Systems and Time Series Analysis Diverse Scientific and Economic Studies

Abstract

This paper considers the asymptotic properties of some unit root test statistics with the errors belonging to the domain of attraction of a symmetric α-stable law with 0 < α < 2. The results obtained can be viewed as a parallel extension of the asymptotic results for the finite-variance case. The test statistics considered are the Dickey-Fuller, the Lagrange multiplier, the Durbin-Watson and Phillips-type modified. Their asymptotic distributions are expressed as functionals of a standard symmetric α-stable Lévy motion. Percentiles of these test statistics are obtained by computer simulation. Asymptotic distributions of sample moments that are part of the test statistics are found to have explicit densities. A small Monte Carlo simulation study is performed to assess small-sample performance of these test statistics for heavy-tailed errors.

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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 1981Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root 1965The Behavior of Stock-Market Prices 1987Time Series Regression with a Unit Root 1996G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance 1967The Variation of Some Other Speculative Prices 1985Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities

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2016A reexamination of stock return predictability 2011A class of simple distribution-free rank-based unit root tests 2003Asymptotic inference in time series regressions with a unit root and infinite variance errors

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