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Some curious power properties of long-horizon tests

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  • Hjalmarsson, Erik

Abstract

Based on simulations and asymptotic results, I highlight three distinct properties of long-horizon predictive tests. (i) The asymptotic power of long-horizon tests increases only with the sample size relative to the forecasting horizon. Keeping this ratio fixed as the sample size increases does not lead to any power gains asymptotically. (ii) Although the power of long-horizon tests increases with the magnitude of the slope coefficient for alternatives close to the null hypothesis, there are no gains in power as the slope coefficient grows large. That is, the power curve is asymptotically horizontal when viewed as a function of the slope coefficient. (iii) For endogenous regressors—i.e., when the innovations to the regressand are contemporaneously correlated with the innovations to the regressor—traditional tests based on the standard long-run OLS estimator result in power curves that are sometimes decreasing in the magnitude of the slope coefficient.

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  • Hjalmarsson, Erik, 2012. "Some curious power properties of long-horizon tests," Finance Research Letters, Elsevier, vol. 9(2), pages 81-91.
    • Handle: RePEc:eee:finlet:v:9:y:2012:i:2:p:81-91
    DOI: 10.1016/j.frl.2011.10.001
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    References listed on IDEAS

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    1. Campbell, John Y., 2001. "Why long horizons? A study of power against persistent alternatives," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 459-491, December.
    2. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    3. Hjalmarsson, Erik, 2011. "New Methods for Inference in Long-Horizon Regressions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(3), pages 815-839, June.
    4. Hjalmarsson, Erik, 2008. "Interpreting long-horizon estimates in predictive regressions," Finance Research Letters, Elsevier, vol. 5(2), pages 104-117, June.
    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    6. David E. Rapach & Mark E. Wohar, 2005. "Valuation ratios and long‐horizon stock price predictability," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 327-344, March.
    7. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    8. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
    9. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
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    Cited by:

    1. 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).
    2. Maynard, Alex & Ren, Dongmeng, 2019. "The finite sample power of long-horizon predictive tests in models with financial bubbles," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 418-430.
    3. Erik Hjalmarsson & Tamas Kiss, 2022. "Long‐run predictability tests are even worse than you thought," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1334-1355, November.

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    More about this item

    Keywords

    Power properties; Predictive regressions; Long-horizon regressions; Stock return predictability;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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