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Semiparametric testing with highly persistent predictors

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  • Werker, Bas J.M.
  • Zhou, Bo

Abstract

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a structural representation of the limit experiment and exploiting invariance relationships therein, we construct invariant point-optimal tests for the regression coefficient of interest. This approach naturally leads to a family of feasible tests based on the component-wise ranks of the innovations that can gain considerable power relative to existing tests under non-Gaussian innovation distributions, while behaving equivalently under Gaussianity. When an i.i.d. assumption on the innovations is appropriate for the data at hand, our tests exploit the efficiency gains possible. Moreover, we show by simulation that our test remains well behaved under some forms of conditional heteroskedasticity.

Suggested Citation

  • Werker, Bas J.M. & Zhou, Bo, 2022. "Semiparametric testing with highly persistent predictors," Journal of Econometrics, Elsevier, vol. 227(2), pages 347-370.
  • Handle: RePEc:eee:econom:v:227:y:2022:i:2:p:347-370
    DOI: 10.1016/j.jeconom.2021.03.016
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    References listed on IDEAS

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    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
    2. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    3. Moreira, Marcelo J. & Mourão, Rafael & Moreira, Humberto Ataíde, 2016. "A critical value function approach, with an application to persistent time-series," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 778, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    4. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    5. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    6. Peter C. B. Phillips, 2014. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Econometrica, Econometric Society, vol. 82(3), pages 1177-1195, May.
    7. 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.
    8. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    9. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    10. 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.
    11. 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.
    12. Kagan, Abram & Landsman, Zinoviy, 1999. "Relation between the covariance and Fisher information matrices," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 7-13, March.
    13. Delphine Cassart & Marc Hallin & Davy Paindaveine, 2010. "On the estimation of cross-information quantities in rank-based inference," Working Papers ECARES ECARES 2010-010, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. Bo Zhou, 2023. "Semiparametrically Optimal Cointegration Test," Papers 2305.08880, arXiv.org.
    2. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    3. Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.

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    More about this item

    Keywords

    Predictive regression; Limit experiment; LABF; Maximal invariant; Rank statistics;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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