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A bootstrap stationarity test for predictive regression invalidity

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  • Iliyan Georgiev
  • David I. Harvey
  • Stephen J. Leybourne
  • A. M. Robert Taylor

Abstract

In order for predictive regression tests to delivery asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that the predictability of the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid with the result that both the finite sample and asymptotic size of the predictability tests can be significantly inflated, with the potential therefore to spuriously indicate predictability. In response we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroskedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic distribution of the bootstrap statistic, conditional on the data, is the same (to first-order) as the asymptotic null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors the validity of the fixed aggressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have important applications beyond the present context. An illustration is given by re-examining the results relating to US stock return data in Campbell and Yogo (2006).

Suggested Citation

  • Iliyan Georgiev & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2017. "A bootstrap stationarity test for predictive regression invalidity," Discussion Papers 17/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:17/04
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    File URL: https://www.nottingham.ac.uk/research/groups/grangercentre/documents/17-04.pdf
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    Cited by:

    1. Giuseppe Cavaliere & Iliyan Georgiev, 2020. "Inference Under Random Limit Bootstrap Measures," Econometrica, Econometric Society, vol. 88(6), pages 2547-2574, November.
    2. Yang, Bingduo & Long, Wei & Yang, Zihui, 2022. "Testing predictability of stock returns under possible bubbles," Journal of Empirical Finance, Elsevier, vol. 68(C), pages 246-260.
    3. Xiaohui Liu & Yuzi Liu & Yao Rao & Fucai Lu, 2021. "A Unified test for the Intercept of a Predictive Regression Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(2), pages 571-588, April.
    4. Christis Katsouris, 2023. "Predictability Tests Robust against Parameter Instability," Papers 2307.15151, arXiv.org.
    5. Demetrescu, Matei & Georgiev, Iliyan & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2023. "Extensions to IVX methods of inference for return predictability," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Demetrescu, Matei & Rodrigues, Paulo M.M., 2022. "Residual-augmented IVX predictive regression," Journal of Econometrics, Elsevier, vol. 227(2), pages 429-460.
    7. Zhou, Weilun & Gao, Jiti & Harris, David & Kew, Hsein, 2024. "Semi-parametric single-index predictive regression models with cointegrated regressors," Journal of Econometrics, Elsevier, vol. 238(1).
    8. Georgiev, Iliyan & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2018. "Testing for parameter instability in predictive regression models," Journal of Econometrics, Elsevier, vol. 204(1), pages 101-118.
    9. Demetrescu, Matei & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2023. "Transformed regression-based long-horizon predictability tests," Journal of Econometrics, Elsevier, vol. 237(2).
    10. Demetrescu, Matei & Georgiev, Iliyan & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2022. "Testing for episodic predictability in stock returns," Journal of Econometrics, Elsevier, vol. 227(1), pages 85-113.
    11. Fukang Zhu & Mengya Liu & Shiqing Ling & Zongwu Cai, 2020. "Testing for Structural Change of Predictive Regression Model to Threshold Predictive Regression Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202021, University of Kansas, Department of Economics, revised Dec 2020.

    More about this item

    Keywords

    Predictive regression; Granger causality; persistence; stationarity test; fixed regressor wild boodstrap; conditional distribution;
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