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Modified Unit Root Tests with Nuisance Parameter Free Asymptotic Distributions

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Abstract

It is well-known that the asymptotic distributions of the Dickey-Fuller (DF) tests for a unit root with linear process errors are not free of nuisance parameters. In this paper, we introduce a consistent estimator for the nuisance parameters and then use it to modify the DF tests, denoted as R-tests. Under fairly mild moment and summability conditions on the errors, we show that the asymptotic distributions of the R-tests are of the same as the Dickey-Fuller distributions. In Monte Carlo experiments, the R-tests are shown to have improved size properties.

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Correspondence to Gaowen Wang.

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Wang, G. Modified Unit Root Tests with Nuisance Parameter Free Asymptotic Distributions. Methodol Comput Appl Probab 19, 519–538 (2017). https://doi.org/10.1007/s11009-016-9498-3

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  • DOI: https://doi.org/10.1007/s11009-016-9498-3

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