Hostname: page-component-5d59c44645-l48q4 Total loading time: 0 Render date: 2024-03-03T18:25:56.596Z Has data issue: false hasContentIssue false

New Methods for Inference in Long-Horizon Regressions

Published online by Cambridge University Press:  18 February 2011

Erik Hjalmarsson*
Affiliation:
Queen Mary, University of London, School of Economics and Finance, Mile End Road, London E1 4NS, UK. e.hjalmarsson@qmul.ac.uk

Abstract

I develop new results for long-horizon predictive regressions with overlapping observations. I show that rather than using autocorrelation 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 ordinary least squares (OLS) estimator suffers from the same problems as the short-run OLS estimator, and it is shown how similar corrections and test procedures as those proposed for the short-run case can also be implemented in the long run. An empirical application to stock return predictability shows that, contrary to many popular beliefs, evidence of predictability does not typically become stronger at longer forecasting horizons.

Type
Research Articles
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amihud, Y., and Hurvich, C. M.. “Predictive Regressions: A Reduced-Bias Estimation Method.” Journal of Financial and Quantitative Analysis, 39 (2004), 813841.Google Scholar
Ang, A., and Bekaert, G.. “Stock Return Predictability: Is It There?Review of Financial Studies, 20 (2007), 651707.Google Scholar
Baker, M.; Taliaferro, R.; and Wurgler, J.. “Predicting Returns with Managerial Decision Variables: Is There a Small-Sample Bias?Journal of Finance, 61 (2006), 17111730.Google Scholar
Berkowitz, J., and Giorgianni, L.. “Long-Horizon Exchange Rate Predictability?Review of Economics and Statistics, 83 (2001), 8191.Google Scholar
Boudoukh, J., and Richardson, M.. “Stock Returns and Inflation: A Long-Horizon Perspective.” American Economic Review, 83 (1993), 13461355.Google Scholar
Boudoukh, J.; Richardson, M.; and Whitelaw, R. F.. “The Myth of Long-Horizon Predictability.” Review of Financial Studies, 21 (2008), 15771605.Google Scholar
Campbell, J. Y. “Why Long Horizons? A Study of Power Against Persistent Alternatives.” Journal of Empirical Finance, 8 (2001), 459491.Google Scholar
Campbell, J. Y., and Shiller, R.. “Stock Prices, Earnings, and Expected Dividends.” Journal of Finance, 43 (1988), 661676.Google Scholar
Campbell, J. Y., and Yogo, M.. “Efficient Tests of Stock Return Predictability.” Journal of Financial Economics, 81 (2006), 2760.Google Scholar
Cavanagh, C. L.; Elliot, G.; and Stock, J. H.. “Inference in Models with Nearly Integrated Regressors.” Econometric Theory, 11 (1995), 11311147.Google Scholar
Chen, W. W., and Deo, R. S.. “Bias Reduction and Likelihood-Based Almost Exactly Sized Hypothesis Testing in Predictive Regressions Using the Restricted Likelihood.” Econometric Theory, 25 (2009a), 11431179.Google Scholar
Chen, W. W., and Deo, R. S.. “The Restricted Likelihood Ratio Test at the Boundary in Autoregressive Series.” Journal of Time Series Analysis, 30 (2009b), 618630.Google Scholar
Elliot, G.; Rothenberg, T. J.; and Stock, J. H.. “Efficient Tests for an Autoregressive Unit Root.” Econometrica, 64 (1996), 813836.Google Scholar
Fama, E. F., and French, K. R.. “Dividend Yields and Expected Stock Returns.” Journal of Financial Economics, 22 (1988), 325.Google Scholar
Fisher, M. E., and Seater, J. J.. “Long-Run Neutrality and Superneutrality in an ARIMA Framework.” American Economic Review, 83 (1993), 402415.Google Scholar
Goyal, A., and Welch, I.. “A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.” Review of Financial Studies, 21 (2008), 14551508.Google Scholar
Hansen, L. P., and Hodrick, R. J.. “Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis.” Journal of Political Economy, 88 (1980), 829853.Google Scholar
Hjalmarsson, E.Fully Modified Estimation with Nearly Integrated Regressors.” Finance Research Letters, 4 (2007), 9294.Google Scholar
Kalbfleisch, J. D., and Sprott, D. A.. “Application of Likelihood Methods to Models Involving Large Numbers of Parameters.” Journal of the Royal Statistical Society B, 32 (1970), 175194.Google Scholar
Lewellen, J.Predicting Returns with Financial Ratios.” Journal of Financial Economics, 74 (2004), 209235.Google Scholar
Mark, N. C. “Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability.” American Economic Review, 85 (1995), 201218.Google Scholar
Mishkin, F. S. “What Does the Term Structure Tell Us About Future Inflation?Journal of Monetary Economics, 25 (1990), 7795.Google Scholar
Mishkin, F. S. “Is the Fisher Effect for Real? A Reexamination of the Relationship between Inflation and Interest Rates.” Journal of Monetary Economics, 30 (1992), 195215.Google Scholar
Nelson, C. R., and Kim, M. J.. “Predictable Stock Returns: The Role of Small Sample Bias.” Journal of Finance, 48 (1993), 641661.Google Scholar
Newey, W. K., and West, K. D.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703708.Google Scholar
Paye, B. S., and Timmermann, A.. “Instability of Return Prediction Models.” Journal of Empirical Finance, 13 (2006), 274315.Google Scholar
Phillips, P. C. B. “Towards a Unified Asymptotic Theory of Autoregression.” Biometrika, 74 (1987), 535547.Google Scholar
Phillips, P. C. B. “Regression Theory for Near-Integrated Time Series.” Econometrica, 56 (1988), 10211043.Google Scholar
Phillips, P. C. B. “Optimal Inference in Cointegrated Systems.” Econometrica, 59 (1991), 283306.Google Scholar
Rossi, B.Testing Long-Horizon Predictive Ability with High Persistence, and the Meese-Rogoff Puzzle.” International Economic Review, 46 (2005), 6192.Google Scholar
Stambaugh, R. F. “Predictive Regressions.” Journal of Financial Economics, 54 (1999), 375421.Google Scholar
Stock, J. H. “Confidence Intervals for the Largest Autoregressive Root in U.S. Economic Time Series.” Journal of Monetary Economics, 28 (1991), 435459.Google Scholar
Torous, W.; Valkanov, R.; and Yan, S.. “On Predicting Stock Returns with Nearly Integrated Explanatory Variables.” Journal of Business, 77 (2004), 937966.Google Scholar
Valkanov, R.Long-Horizon Regressions: Theoretical Results and Applications.” Journal of Financial Economics, 68 (2003), 201232.Google Scholar