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Some curious power properties of long-horizon tests

  • Hjalmarsson, Erik

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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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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  1. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  2. Campbell, John & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Scholarly Articles 3122601, Harvard University Department of Economics.
  3. Campbell, John, 2001. "Why Long Horizons? A Study of Power Against Persistent Alternatives," Scholarly Articles 3196341, Harvard University Department of Economics.
  4. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  5. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  6. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  7. 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.
  8. Hjalmarsson, Erik, 2008. "Interpreting long-horizon estimates in predictive regressions," Finance Research Letters, Elsevier, vol. 5(2), pages 104-117, June.
  9. 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.
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