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Published online by Cambridge University Press:  27 October 2014

Zongwu Cai*
University of Kansas and Xiamen University
Yunfei Wang
Sun Trust Bank
Yonggang Wang
First Tennessee Bank
*Address correspondence to Zongwu Cai, Department of Economics, University of Kansas, Lawrence, KS 66045, USA; e-mail:


It is well known that allowing the coefficients to be time-varying in a predictive model with possibly nonstationary regressors can help to deal with instability in predictability associated with linear predictive models. In this paper, an L2-type test statistic is proposed to test the stability of the coefficient vector, and the asymptotic distributions of the proposed test statistic are developed under both null and alternative hypotheses. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed test statistic and an empirical example is examined to demonstrate the practical application of the proposed testing method.

Copyright © Cambridge University Press 2014 

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Amihud, Y. & Hurvich, C. (2004) Predictive regression: A reduced-bias estimation method. Journal of Financial and Quantitative Analysis 39, 813841.CrossRefGoogle Scholar
Amihud, Y., Hurvich, C., & Wang, Y. (2009) Multiple-predictor regressions: Hypothesis testing. Review of Financial Studies 22, 413434.CrossRefGoogle Scholar
Cai, Z. (2007) Trending time varying coefficient time series models with serially correlated errors. Journal of Econometrics 137, 163188.CrossRefGoogle Scholar
Cai, Z. & Wang, Y. (2014) Testing predictive regression models with nonstationary regressors. Journal of Econometrics 178, 414.CrossRefGoogle Scholar
Campbell, J. & Yogo, M. (2006) Efficient tests of stock return predictability. Journal of Financial Econometrics 81, 2760.CrossRefGoogle Scholar
Cavanagh, C.L., Elliott, G., & Stock, J.H. (1995) Inference in models with nearly integrated regressors. Econometric Theory 11, 11311147.CrossRefGoogle Scholar
Chen, B. & Hong, Y. (2012) Testing for smooth structural changes in time series models via nonparametric regression. Econometrica 80, 11571183.Google Scholar
Fan, Y. & Li, Q. (1996) Consistent model specification tests: Omitted variables and semiparametric functional forms. Econometrica 65, 865890.CrossRefGoogle Scholar
Fan, Y. & Li, Q. (1999) Central limit theorem for degenerate U-statistic of absolutely regular process: With an application to model specification testing. Journal of Nonparametric Statistics 10, 245271.CrossRefGoogle Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Applications. Academic Press.Google Scholar
Hamilton, J.D. (1994) Time Series Analysis. Princeton University Press.Google Scholar
Hansen, B.E. (2001) The new econometrics of structural change: Dating breaks in U.S. labor productivity. Journal of Economic Perspectives 15, 117128.CrossRefGoogle Scholar
Kothari, S.P. & Shanken, J. (1997) Book-to-market, dividend yield, and expected market returns: A time-series analysis. Journal of Financial Economics 44, 169203.CrossRefGoogle Scholar
Lewellen, J. (2004) Predicting returns with financial ratios. Journal of Financial Economics 74, 209235.CrossRefGoogle Scholar
Li, Q., Huang, C.J., Li, D., & Fu, T. (2002) Semiparametric smooth coefficient model. Journal of Business and Economics Statistics 20, 412422.CrossRefGoogle Scholar
Park, J.Y. & Hahn, S.B. (1999) Cointegrating regressions with time varying coefficients. Econometric Theory 15, 664703.CrossRefGoogle Scholar
Paye, B.S. & Timmermann, A. (2006) Instability of return prediction models. Journal of Empirical Finance 13, 274315.CrossRefGoogle Scholar
Phillips, P.C.B. (1988) Regression theory for near-integrated time series. Econometrica 56, 10211043.CrossRefGoogle Scholar
Phillips, P.C.B. (2014) On confidence intervals for autoregressive roots and predictive regression. Econometrica 82, 11771195.Google Scholar
Phillips, P.C.B & Lee, J.H. (2013) Predictive regression under various degrees of persistence and robust long horizon regression. Journal of Econometrics 177, 250264.CrossRefGoogle Scholar
Phillips, P.C.B., Li, D., & Gao, J. (2013). Estimating Smooth Structural Change in Cointegration Models. Discussion paper no. 1910, Cowles Foundations, Yale University.
Rio, E. (1995) The functional law of the iterated logarithm for stationary strongly mixing sequences. Annals of Probability 23, 11881203.CrossRefGoogle Scholar
Robinson, P.M. (1989) Nonparametric estimation of time-varying parameters. In Hackled, P. & Westland, A.H. (eds.), Statistical Analysis and Forecasting of Economic Structural Change, pp. 253264. Springer-Verlag.CrossRefGoogle Scholar
Robinson, P.M. (1991) Time-varying nonlinear regression. In Hackled, P. & Westland, A.H. (eds.), Economic Structure Change, Analysis and Forecasting, pp. 179190. Springer-Verlag.Google Scholar
Stambaugh, R. (1999) Predictive regressions. Journal of Financial Economics 54, 375421.CrossRefGoogle Scholar
Sun, Y., Cai, Z., & Li, Q. (2008) Consistent Nonparametric Test on Parametric Smooth Coefficient Model with Nonstationary Data. Working paper, Department of Economics, University of Guelph.
Torous, W., Valkanov, R., & Yan, S. (2004) On predicting stock returns with nearly integrated explanatory variables. Journal of Business 77, 937966.CrossRefGoogle Scholar
Wang, Y. (2010) Essays on predictive regression models for asset returns. Ph.D. dissertation, University of North Carolina at Charlotte.
Wang, Q. & Phillips, P.C.B. (2012) A specification test for nonlinear nonstationary models. Annals of Statistics 40, 727758.CrossRefGoogle Scholar
Wu, L. (2013) Consistent nonparametric test on nonlinear regression models with nearly integrated covariates. Ph.D. dissertation, University of North Carolina at Charlotte.
Xiao, Z. (2009) Functional coefficient co-integration models. Journal of Econometrics 152, 8192.CrossRefGoogle Scholar
Zheng, J.X. (1996) A consistent test of functional form via nonparametric estimation technique. Journal of Econometrics 75, 263289.CrossRefGoogle Scholar
Zhu, F., Cai, Z., & Peng, L. (2014) Predictive regressions for macroeconomics data. The Annals of Applied Statistics 8, 577594.CrossRefGoogle Scholar