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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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Bibliographic Info

Article provided by Elsevier in its journal Finance Research Letters.

Volume (Year): 9 (2012)
Issue (Month): 2 ()
Pages: 81-91

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Handle: RePEc:eee:finlet:v:9:y:2012:i:2:p:81-91

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Web page: http://www.elsevier.com/locate/frl

Related research

Keywords: Power properties; Predictive regressions; Long-horizon regressions; Stock return predictability;

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References

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  1. Mark E. Wohar & David E. Rapach, 2005. "Valuation ratios and long-horizon stock price predictability," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 327-344.
  2. Stambaugh, Robert F., 1999. "Predictive regressions," Journal of Financial Economics, Elsevier, vol. 54(3), pages 375-421, December.
  3. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  4. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  5. Campbell, John, 2001. "Why Long Horizons? A Study of Power Against Persistent Alternatives," Scholarly Articles 3196341, Harvard University Department of Economics.
  6. Hjalmarsson, Erik, 2011. "New Methods for Inference in Long-Horizon Regressions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(03), pages 815-839, June.
  7. Campbell, John & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Scholarly Articles 3122601, Harvard University Department of Economics.
  8. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  9. Hjalmarsson, Erik, 2008. "Interpreting long-horizon estimates in predictive regressions," Finance Research Letters, Elsevier, vol. 5(2), pages 104-117, June.
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