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Long Memory Regressors and Predictive Testing: A Two-stage Rebalancing Approach

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  • Alex Maynard
  • Aaron Smallwood
  • Mark E. Wohar

Abstract

Predictability tests with long memory regressors may entail both size distortion and incompatibility between the orders of integration of the dependent and independent variables. Addressing both problems simultaneously, this paper proposes a two-step procedure that rebalances the predictive regression by fractionally differencing the predictor based on a first-stage estimation of the memory parameter. Extensive simulations indicate that our procedure has good size, is robust to estimation error in the first stage, and can yield improved power over cases in which an integer order is assumed for the regressor. We also extend our approach beyond the standard predictive regression context to cases in which the dependent variable is also fractionally integrated, but not cointegrated with the regressor. We use our procedure to provide a valid test of forward rate unbiasedness that allows for a long memory forward premium.

Suggested Citation

  • Alex Maynard & Aaron Smallwood & Mark E. Wohar, 2013. "Long Memory Regressors and Predictive Testing: A Two-stage Rebalancing Approach," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 318-360, November.
    • Handle: RePEc:taf:emetrv:v:32:y:2013:i:3:p:318-360
    DOI: 10.1080/07474938.2012.690663
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
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    2. Daniela Osterrieder & Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés, 2015. "Unbalanced Regressions and the Predictive Equation," CREATES Research Papers 2015-09, Department of Economics and Business Economics, Aarhus University.
    3. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    4. Chen, Yong & Eaton, Gregory W. & Paye, Bradley S., 2018. "Micro(structure) before macro? The predictive power of aggregate illiquidity for stock returns and economic activity," Journal of Financial Economics, Elsevier, vol. 130(1), pages 48-73.
    5. Kruse Robinson & Ventosa-Santaulària Daniel & Noriega Antonio E., 2017. "Changes in persistence, spurious regressions and the Fisher hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-28, June.
    6. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    7. Aistis Raudys & Edvinas Goldstein, 2022. "Forecasting Detrended Volatility Risk and Financial Price Series Using LSTM Neural Networks and XGBoost Regressor," JRFM, MDPI, vol. 15(12), pages 1-12, December.
    8. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    9. Jayawardena, Nirodha I. & Todorova, Neda & Li, Bin & Su, Jen-Je & Gau, Yin-Feng, 2022. "Risk-return trade-off in the Australian Securities Exchange: Accounting for overnight effects, realized higher moments, long-run relations, and fractional cointegration," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 384-401.
    10. Hualde, Javier, 2014. "Estimation of long-run parameters in unbalanced cointegration," Journal of Econometrics, Elsevier, vol. 178(2), pages 761-778.
    11. Torben G. Andersen & Rasmus T. Varneskov, 2018. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    12. Robin Dee & Armin Fügenschuh & George Kaimakamis, 2021. "The Unit Re-Balancing Problem," Mathematics, MDPI, vol. 9(24), pages 1-19, December.
    13. Chen, Cathy Yi-Hsuan & Chiang, Thomas C. & Härdle, Wolfgang Karl, 2018. "Downside risk and stock returns in the G7 countries: An empirical analysis of their long-run and short-run dynamics," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 21-32.
    14. Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, Department of Economics and Business Economics, Aarhus University.

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