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New methods for inference in long-run predictive regressions

  • Erik Hjalmarsson

I develop new asymptotic results for long-horizon regressions with overlapping observations. I show that rather than using auto-correlation robust standard errors, the standard t-statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data. Further, when the regressors are persistent and endogenous, the long-run OLS estimator suffers from the same problems as does the short-run OLS estimator, and similar corrections and test procedures as those proposed for the short-run case should also be used in the long-run. In addition, I show that under an alternative of predictability, long-horizon estimators have a slower rate of convergence than short-run estimators and their limiting distributions are non-standard and fundamentally different from those under the null hypothesis. These asymptotic results are supported by simulation evidence and suggest that under standard econometric specifications, short-run inference is generally preferable to long-run inference. The theoretical results are illustrated with an application to long-run stock-return predictability.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 853.

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Date of creation: 2006
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Handle: RePEc:fip:fedgif:853
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  1. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  2. John Y. Campbell, 1993. "Why Long Horizons: A Study of Power Against Persistent Alternatives," NBER Technical Working Papers 0142, National Bureau of Economic Research, Inc.
  3. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-43, September.
  4. Campbell, John & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Scholarly Articles 3122601, Harvard University Department of Economics.
  5. Frederic S. Mishkin, 1988. "What Does the Term Structure Tell Us About Future Inflation?," NBER Working Papers 2626, National Bureau of Economic Research, Inc.
  6. Dean Corbae & Sam Ouliaris & Peter C.B. Phillips, 1997. "Band Spectral Regression with Trending Data," Cowles Foundation Discussion Papers 1163, Cowles Foundation for Research in Economics, Yale University.
  7. Goetzmann, W.N., 1990. "Testing The Predictive Power Of Dividend Yields," Papers fb-_90-12, Columbia - Graduate School of Business.
  8. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
  10. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
  12. Lanne, M., 2000. "Testing the Predictability of Stock Returns," University of Helsinki, Department of Economics 488, Department of Economics.
  13. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  14. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  15. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
  16. Michael Jansson & Marcelo J. Moreira, 2004. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Harvard Institute of Economic Research Working Papers 2047, Harvard - Institute of Economic Research.
  17. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," NBER Working Papers 2511, National Bureau of Economic Research, Inc.
  18. Nelson C. Mark & Donggyu Sul, 2004. "The Use of Predictive Regressions at Alternative Horizons in Finance and Economics," NBER Technical Working Papers 0298, National Bureau of Economic Research, Inc.
  19. Hjalmarsson, Erik, 2007. "Fully modified estimation with nearly integrated regressors," Finance Research Letters, Elsevier, vol. 4(2), pages 92-94, June.
  20. 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.
  21. N. Gregory Mankiw & Matthew D. Shapiro, 1985. "Do We Reject Too Often? Small Sample Properties of Tests of Rational Expectations Models," NBER Technical Working Papers 0051, National Bureau of Economic Research, Inc.
  22. 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.
  23. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  24. Jeremy Berkowitz & Lorenzo Giorgianni, 1996. "Long-horizon exchange rate predictability?," Finance and Economics Discussion Series 96-39, Board of Governors of the Federal Reserve System (U.S.).
  25. 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.
  26. Polk, Christopher & Thompson, Samuel & Vuolteenaho, Tuomo, 2006. "Cross-sectional forecasts of the equity premium," Journal of Financial Economics, Elsevier, vol. 81(1), pages 101-141, July.
  27. 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.
  28. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  29. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
  30. Frederic S. Mishkin, 1991. "Is the Fisher Effect for Real? A Reexamination of the Relationship Between Inflation and Interest Rates," NBER Working Papers 3632, National Bureau of Economic Research, Inc.
  31. 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.
  32. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
  33. Boudoukh, Jacob & Richardson, Matthew, 1993. "Stock Returns and Inflation: A Long-Horizon Perspective," American Economic Review, American Economic Association, vol. 83(5), pages 1346-55, December.
  34. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  35. Daniel, Kent, 2001. "The power and size of mean reversion tests," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 493-535, December.
  36. Richardson, Matthew & Stock, James H., 1989. "Drawing inferences from statistics based on multiyear asset returns," Journal of Financial Economics, Elsevier, vol. 25(2), pages 323-348, December.
  37. Barbara Rossi, 2005. "Testing Long-Horizon Predictive Ability With High Persistence, And The Meese-Rogoff Puzzle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 61-92, 02.
  38. 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.
  39. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
  40. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  41. Walter Torous & Rossen Valkanov & Shu Yan, 2004. "On Predicting Stock Returns with Nearly Integrated Explanatory Variables," The Journal of Business, University of Chicago Press, vol. 77(4), pages 937-966, October.
  42. 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.
  43. Jacob Boudoukh & Matthew Richardson & Robert Whitelaw, 2005. "The Myth of Long-Horizon Predictability," NBER Working Papers 11841, National Bureau of Economic Research, Inc.
  44. Andrew Ang & Geert Bekaert, 2001. "Stock Return Predictability: Is it There?," NBER Working Papers 8207, National Bureau of Economic Research, Inc.
  45. Fisher, Mark E & Seater, John J, 1993. "Long-Run Neutrality and Superneutrality in an ARIMA Framework," American Economic Review, American Economic Association, vol. 83(3), pages 402-15, June.
  46. 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.
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