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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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    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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