Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T21:19:20.261Z Has data issue: false hasContentIssue false
  • English
  • Français

COVARIANCE-BASED ORTHOGONALITY TESTS FOR REGRESSORS WITH UNKNOWN PERSISTENCE

Published online by Cambridge University Press:  01 February 2009

Alex Maynard and
Katsumi Shimotsu
Alex Maynard*
Affiliation:
University of Guelph
Katsumi Shimotsu*
Affiliation:
Queen's University
*
*Address correspondence to Alex Maynard, Department of Economics, McKinnan Building, University of Guelph, Guelph, ON N1G 2W1, Canada; e-mail: maynarda@uoguelph.ca.
†Katsumi Shimotsu, 229 Dunning Hall, Department of Economics, Queen's University, Kingston, ON K7L 3N6, Canada; e-mail: shimotsu@econ.queensu.ca.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard predictive regression tests can suffer from well-documented size distortion. Moreover, under the alternative hypothesis, they force the dependent variable to share the same order of integration as the predictor, whereas in practice the dependent variable often appears stationary and the predictor may be near-nonstationary. By contrast, the new test does not enforce the same orders of integration and is therefore capable of detecting a rich set of alternatives to orthogonality that are excluded by the standard predictive regression model. Moreover, the test statistic has a standard normal limit distribution for both unit root and local-to-unity conditioning variables, without prior knowledge of the local-to-unity parameter. If the conditioning variable is stationary, the test remains conservative and consistent. Simulations suggest good small-sample performance. As an empirical application, we test for the predictability of stock returns using two persistent predictors, the dividend-price ratio and short-term interest rate.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009, pp. 63 - 116
Copyright
Copyright © Cambridge University Press 2009

References

REFERENCES

Amihud, Y. & Hurvich, C.M. (2004) Predictive regressions: A reduced-bias estimation method. Journal of Financial and Quantitative Analysis 39, 813–841.CrossRefGoogle Scholar
Amihud, Y., Hurvich, C.M., & Wang, Y. (2004) Hypothesis Testing in Predictive Regressions. Mimeo. New York University.Google Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance estimation. Econometrica 59, 817–858.CrossRefGoogle Scholar
Ang, A& Bekaert, G. (2007) Stock return predictability: Is it there? Review of Financial Studies 20, 651–707.CrossRefGoogle Scholar
Brown, B.M. (1971) Martingale central limit theorems. Annals of Mathematical Statistics 42, 59–66.CrossRefGoogle Scholar
Campbell, B& Dufour, J.M. (1997) Exact nonparametric tests of orthogonality and random walk in the presence of a drift parameter. International Economic Review 38, 151–173.CrossRefGoogle Scholar
Campbell, J, Lo, A. & MacKinlay, C. (1997) The Econometrics of Financial Markets. Princeton University Press.CrossRefGoogle Scholar
Campbell, J& Yogo, M. (2006) Efficient tests of stock return predictability. Journal of Financial Economics 81, 27–60.CrossRefGoogle Scholar
Campbell, J.Y. & Shiller, R.J. (1988a) The dividend price ratio and expectations of future dividends and discount factors. Review of Financial Studies 1, 195–227.CrossRefGoogle Scholar
Campbell, J.Y. & Shiller, R.J. (1988b) Stock prices, earnings, and expected dividends. Journal of Finance 43, 661–676.CrossRefGoogle Scholar
Cavanagh, C.L., Elliott, G., & Stock, J. (1995) Inference in models with nearly integrated regressors. Econometric Theory 11, 1131–1147.CrossRefGoogle Scholar
Dufour, J.M. & Pelletier, D. (2002) Linear estimation of weak VARMA models with a macro- economic application. In ASA Proceedings, Business and Economic Statistics, pp. 2659–2664.Google Scholar
Elliott, G. (1998) On the robustness of cointegration methods when regressors have almost unit roots. Econometrica 66, 149–158.CrossRefGoogle Scholar
Elliott, G. & Stock, J. (1994) Inference in time series regression when the order of integration of a regressor is unknown. Econometric Theory 10, 672–700.CrossRefGoogle Scholar
Fama, E. & French, K. (1988) Permanent and temporary components of stock prices. Journal of Political Economy 96, 246–273.CrossRefGoogle Scholar
Goetzmann, W. & Jorion, P. (1993) Testing the predictive power of dividend yields. Journal of Finance 48, 663–670.CrossRefGoogle Scholar
Hannan, E.J. (1970) Multiple Time Series. Wiley.CrossRefGoogle Scholar
Hodrick, R. (1992) Dividend yields and expected stock returns: Alternative procedures for inference and measurement. Review of Financial Studies 5, 357–368.CrossRefGoogle Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 1449–1459.CrossRefGoogle Scholar
Jansson, M. & Moreira, M.J. (2006) Optimal inference in regression models with nearly integrated regressors. Econometrica 74, 681–714.CrossRefGoogle Scholar
Lanne, M. (2002) Testing the predictability of stock returns. Review of Economics and Statistics 84, 407–415.CrossRefGoogle Scholar
Lewellen, J. (2004) Predicting returns with financial ratios. Journal of Financial Economics 74, 209–235.CrossRefGoogle Scholar
Mankiw, N. & Shapiro, M. (1986) Do we reject too often? Small sample properties of tests of rational expectations models. Economics Letters 20, 139–145.Google Scholar
Marmer, V. (2008) Nonlinearity, nonstationarity and spurious forecasts. Journal of Econometrics, 142, 1–27.CrossRefGoogle Scholar
Maynard, A. (2006) The forward premium anomaly: Statistical artifact or economic puzzle? New evidence from robust tests. Canadian Journal of Economics 39, 1244–1281.CrossRefGoogle Scholar
Moon, R., Rubiya, A. & Valkanov, R. (2004) Long-horizon regressions when the predictor is slowly varying. Mimeo, Rady Sehoo of Management, University of California at San Diego.CrossRefGoogle Scholar
Nelson, C. & Kim, M (1993) Predictable stock returns: The role of small sample bias. Journal of Finance 48, 641–661.CrossRefGoogle Scholar
Ng, S. & Perron, P. (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554.CrossRefGoogle Scholar
Phillips, P.C.B. (1999) Discrete Fourier Transforms of Fractional Processes, Cowles Foundation Discussion paper #1243, Yale University.Google Scholar
Phillips, P.C.B. (2005) Challenges of trending time series econometrics. Mathematics and Computers in Simulation 68, 401–416.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Priestley, M.B. (1981) Spectral Analysis and Time Series. Academic Press.Google Scholar
Rudebusch, G.D. (1992) Trends and random walks in macroeconomic time series: A reexamination. International Economic Review 33, 661–680.CrossRefGoogle Scholar
Saikkonen, P. & Lütkepohl, H. (1996) Infinite-order cointegrated vector autoregressive processes. Econometric Theory 12, 814–844.CrossRefGoogle Scholar
Shiller, R. (1984) Stock prices and social dynamics. Brookings Papers on Economic Activity 2, 457–498.CrossRefGoogle Scholar
Stambaugh, R. (1986) Bias in Regressions with Lagged Stochastic Regressors, Center for Research in Security Prices Working paper 156, University of Chicago.Google Scholar
Stambaugh, R. (1999) Predictive regressions. Journal of Financial Economics 54, 375–421.CrossRefGoogle Scholar
Stock, J. (1991) Confidence intervals for the largest autoregressive root in U.S. economic time series. Journal of Monetary Economics 28, 435–460.CrossRefGoogle Scholar
Toda, H.Y. & Yamamoto, T. (1995) Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics 66, 225–250.CrossRefGoogle Scholar
Torous, W., Valkanov, R. & Yan, S. (2005) On predicting stock returns with nearly integrated explanatory variables. Journal of Business 77, 937–966.CrossRefGoogle Scholar
Valkanov, R. (2003) Long-horizon regressions: Theoretical results and applications. Journal of Financial Economics 68, 201–232.CrossRefGoogle Scholar
Viceira, L. (1997) Testing for Structural Change in the Predictability of Asset Returns. Mimeo, Harvard University.Google Scholar
Wolf, M. (2000) Stock returns and dividend yields revisited: A new way to look at an old problem. Journal of Business & Economic Statistics 18, 18–30.CrossRefGoogle Scholar
Wright, J. (2000) Confidence sets for cointegrating coefficients based on stationarity tests. Journal of Business & Economic Statistics 18, 211–222.CrossRefGoogle Scholar