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Why Long Horizons? A Study of Power Against Persistent Alternatives

  • Campbell, John

This paper studies tests of predictability in regressions with a given AR(1) regressor and an asset return dependent variable measured over a short or long horizon. The paper shows that when there is a persistent predictable component in the return, an increase in the horizon may increase the R2 statistic of the regression and the approximate slope of a predictability test. Monte Carlo experiments show that long-horizon regression tests have serious size distortions when asymptotic critical values are used, but some versions of such tests have power advantages remaining after size is corrected.

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File URL: http://dash.harvard.edu/bitstream/handle/1/3196341/campbellnber_longhorizons.pdf
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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3196341.

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Date of creation: 2001
Date of revision:
Publication status: Published in Journal of Empirical Finance
Handle: RePEc:hrv:faseco:3196341
Contact details of provider: Postal: Littauer Center, Cambridge, MA 02138
Phone: 617-495-2144
Fax: 617-495-7730
Web page: http://www.economics.harvard.edu/

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  1. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  2. Mishkin, Frederic S, 1990. "The Information in the Longer Maturity Term Structure about Future Inflation," The Quarterly Journal of Economics, MIT Press, vol. 105(3), pages 815-28, August.
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  4. Goetzman, W.N. & Jorion, P., 1992. "Testing the Predictive Power of Dividend Yields," Papers 93-03, Columbia - Graduate School of Business.
  5. Cochrane, John H., 1991. "Volatility tests and efficient markets : A review essay," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 463-485, June.
  6. John Y. Campbell, 1990. "A Variance Decomposition for Stock Returns," NBER Working Papers 3246, National Bureau of Economic Research, Inc.
  7. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  8. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-92, September.
  9. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
  10. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," NBER Working Papers 2511, National Bureau of Economic Research, Inc.
  11. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-74, May.
  12. Nelson, Charles R & Kim, Myung J, 1993. " Predictable Stock Returns: The Role of Small Sample Bias," Journal of Finance, American Finance Association, vol. 48(2), pages 641-61, June.
  13. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
  14. Lo, Andrew W. & MacKinlay, A. Craig, 1989. "The size and power of the variance ratio test in finite samples : A Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 40(2), pages 203-238, February.
  15. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
  16. Campbell, John Y & Shiller, Robert J, 1991. "Yield Spreads and Interest Rate Movements: A Bird's Eye View," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 495-514, May.
  17. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  18. Geweke, John, 1981. "The Approximate Slopes of Econometric Tests," Econometrica, Econometric Society, vol. 49(6), pages 1427-42, November.
  19. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
  20. Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
  21. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
  22. Frederic S. Mishkin, 1988. "What Does the Term Structure Tell Us About Future Inflation?," NBER Working Papers 2626, National Bureau of Economic Research, Inc.
  23. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
  24. Smith, T. & Richardson, M., 1991. "Robust Power Calculations With tests for Serial Correlation in stock Returns," Weiss Center Working Papers 12-91, Wharton School - Weiss Center for International Financial Research.
  25. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
  26. Faust, Jon, 1992. "When Are Variance Ratio Tests for Serial Dependence Optimal?," Econometrica, Econometric Society, vol. 60(5), pages 1215-26, September.
  27. Tim Bollerslev & Robert J. Hodrick, 1992. "Financial Market Efficiency Tests," NBER Working Papers 4108, National Bureau of Economic Research, Inc.
  28. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
  29. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
  30. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
  31. Jegadeesh, Narasimhan, 1991. " Seasonality in Stock Price Mean Reversion: Evidence from the U.S. and the U.K," Journal of Finance, American Finance Association, vol. 46(4), pages 1427-44, September.
  32. Robert F. Stambaugh, . "Estimating Conditional Expectations When Volatility Fluctuates," Rodney L. White Center for Financial Research Working Papers 17-93, Wharton School Rodney L. White Center for Financial Research.
  33. Matthew Richardson & Tom Smith, . "Robust Power Calculations with Tests for Serial Correlation in Stock Returns," Rodney L. White Center for Financial Research Working Papers 12-91, Wharton School Rodney L. White Center for Financial Research.
  34. Richardson, Matthew & Smith, Tom, 1991. "Tests of Financial Models in the Presence of Overlapping Observations," Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 227-54.
  35. Matthew Richardson & James H. Stock, 1990. "Drawing Inferences From Statistics Based on Multi-Year Asset Returns," NBER Working Papers 3335, National Bureau of Economic Research, Inc.
  36. Scott, Louis O, 1985. "The Present Value Model of Stock Prices: Regression Tests and Monte Carlo Results," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 599-605, November.
  37. Mark, Nelson C, 1995. "Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability," American Economic Review, American Economic Association, vol. 85(1), pages 201-18, March.
  38. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier.
  39. Fama, Eugene F., 1990. "Term-structure forecasts of interest rates, inflation and real returns," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 59-76, January.
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