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A critical value function approach, with an application to persistent time-series

Author

Listed:
  • Marcelo Moreira

    (Institute for Fiscal Studies and Fundação Getúlio Vargas)

  • Rafael Mourão

    (Institute for Fiscal Studies)

  • Humberto Moreira

    (Institute for Fiscal Studies)

Abstract

Researchers often rely on the t-statistic to make inference on parameters in statistical models. It is common practice to obtain critical values by simulation techniques. This paper proposes a novel numerical method to obtain an approximately similar test. This test rejects the null hypothesis when the test statistic is larger than a critical value function (CVF) of the data. We illustrate this procedure when regressors are highly persistent, a case in which commonly-used simulation methods encounter difficulties controlling size uniformly. Our approach works satisfactorily, controls size, and yields a test which outperforms the two other known similar tests. Supplement for CWP24/16

Suggested Citation

  • Marcelo Moreira & Rafael Mourão & Humberto Moreira, 2016. "A critical value function approach, with an application to persistent time-series," CeMMAP working papers CWP24/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:24/16
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    References listed on IDEAS

    as
    1. Romano, Joseph P & Wolf, Michael, 2001. "Subsampling Intervals in Autoregressive Models with Linear Time Trend," Econometrica, Econometric Society, vol. 69(5), pages 1283-1314, September.
    2. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    3. Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-222, April.
    4. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    5. Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 1-24, March.
    6. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(5), pages 692-745, October.
    7. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
    8. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    9. Moreira, Humberto Ataíde & Moreira, Marcelo J., 2013. "Contributions to the Theory of Optimal Tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 747, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    10. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
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    Citations

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    Cited by:

    1. Werker, Bas J.M. & Zhou, Bo, 2022. "Semiparametric testing with highly persistent predictors," Journal of Econometrics, Elsevier, vol. 227(2), pages 347-370.
    2. Bas Werker & Bo Zhou, 2020. "Semiparametric Testing with Highly Persistent Predictors," Papers 2009.08291, arXiv.org.
    3. Werker, Bas J.M. & Zhou, B., 2022. "Semiparametric testing with highly persistent predictors," Other publications TiSEM 2974ce9c-97c1-44cd-9331-0, Tilburg University, School of Economics and Management.
    4. Kees Jan van Garderen & Noud van Giersbergen, 2020. "A Nearly Similar Powerful Test for Mediation," Papers 2012.11342, arXiv.org, revised Jan 2022.

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