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On the power of bootstrap tests for stationarity: a Monte Carlo comparison

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Abstract

This paper studies the behavior of recently proposed bootstrap tests for the null hypothesis of stationarity when the data are generated under the alternative hypothesis of a unit root. Using Monte Carlo experiments and empirical examples, it is shown that the power of these tests critically depends on the type of bootstrap employed. Specifically, while tests based on the stationary bootstrap have power functions that are increasing with respect to sample size, those based on the sieve bootstrap have non-monotonic power functions. We argue that this difference arises from the fact that the latter procedure does not impose the null hypothesis when generating the bootstrap samples while the former ensures that the bootstrap samples are stationary, conditional on the original data. Our results therefore suggest that while both forms of bootstrap are effective at providing improved distributional approximations under the null hypothesis, it is important to pay careful attention to the particular type of bootstrap being employed when attempting to distinguish between the unit root and stationarity hypotheses as the choice of bootstrap can have crucial implications for the power of the resulting tests.

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Notes

  1. As shown in Kurozumi (2002), this rule ensures that the KPSS test (based on asymptotic critical values) diverges under the alternative while the usual automatic bandwidth rule proposed by Andrews (1991) does not lead to a consistent test statistic.

  2. The optimal choice is defined as the one that minimizes the mean squared error (to an appropriate order) of the variance estimate of the sample mean under the null hypothesis of stationarity.

  3. The qualitative features of the results are not sensitive to the number of Monte Carlo replications or the number of bootstrap replications. For instance, using 10,000 Monte Carlo replications with 999 bootstrap replications or 10,000 Monte Carlo replications with 1,999 replications gave results very similar to those reported in the paper.

  4. Given the large extent of size distortions associated with the asymptotic KPSS tests, the rejection frequencies for these tests are adjusted for size.

  5. We thank an anonymous referee for pointing this out.

  6. The full set of results is available upon request.

  7. The exceptions to the 1957Q1 start date are Austria (1970Q1) and Japan (1966Q4). The exceptions to the 2000Q1 end date are Ireland (1998Q4) and Japan (1999Q3).

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Acknowledgments

We are grateful to two anonymous referees whose comments and suggestions helped improve the paper. We are solely responsible for any errors.

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Authors and Affiliations

  1. Department of Statistics, University of California-Irvine, Bren Hall 2243, Irvine, 92697, USA

    Sevan G. Gulesserian

  2. Krannert School of Management, Purdue University, 403 West State Street, West Lafayette, IN, 47907, USA

    Mohitosh Kejriwal

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  1. Sevan G. Gulesserian
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  2. Mohitosh Kejriwal
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Correspondence to Mohitosh Kejriwal.

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Gulesserian, S.G., Kejriwal, M. On the power of bootstrap tests for stationarity: a Monte Carlo comparison. Empir Econ 46, 973–998 (2014). https://doi.org/10.1007/s00181-013-0711-8

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  • DOI: https://doi.org/10.1007/s00181-013-0711-8

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