A Predictive Functional Regression Model for Asset Return

Affiliation(s)

Wuhan Institute of Technology, Wuhan, China.

University of Science and Technology, Beijing, China.

Wuhan Institute of Technology, Wuhan, China.

University of Science and Technology, Beijing, China.

ABSTRACT

Since many of predictive financial variables are highly persistent and non-stationary, it is challenging econometrically to explore the predictability of asset returns. Predictability issues are generally addressed in parametric regressions [1,2] in which rates of asset returns are regressed against the lagged values of stochastic explanatory variables, but three limitations stand ahead [3-5]. This paper studies a predictive functional regression model for asset returns, which takes account of endogeneity and integrated or nearly integrated explanatory variables. The regression function is expressed in terms of distribution of the vector of the observable variables. Estimators are nonlinear functionals of a kernel estimator for the distribution of the observable variables [6]. We find that the estimators for the distribution of the unobservable random terms and the nonparametric function are consistent and asymptotically normal. This paper obtains the similar results in many literatures, for example [1-5], but in different method.

Cite this paper

X. Dai, H. Li and Y. Wang, "A Predictive Functional Regression Model for Asset Return,"*Journal of Mathematical Finance*, Vol. 3 No. 2, 2013, pp. 307-311. doi: 10.4236/jmf.2013.32030.

X. Dai, H. Li and Y. Wang, "A Predictive Functional Regression Model for Asset Return,"

References

[1] N. G. Mankiw and M. Shapiro, “Do We Reject Too Often? Small Sample Properties of Tests of Rational Expectation models,” Economics Letters, Vol. 20, 1986, pp. 139-145.

[2] R. Stambaugh, “Bias in Regressions with Lagged Stochastic Regressors,” Working Paper, University of Chicago, 1986.

[3] J. Campbell and M. Yogo, “Efficient Tests of Stock Return Predictability,” Journal of Financial Econometrics, Vol. 81, No. 1, 2006, pp. 27-60. doi:10.1016/j.jfineco.2005.05.008

[4] B. S. Paye and A. Timmermann, “Instability of Return Prediction Models,” Journal of Empirical Finance, Vol. 13, No. 3, 2006, pp. 274-315. doi:10.1016/j.jempfin.2005.11.001

[5] T. Dangl and M. Halling, “Predictive Regressions with Time-Varying Coefficients,” Working Paper, School of Business, University of Utah, 2007.

[6] E. A. Nadaraya, “Some New Estimates for Distribution Functions,” Theory of Probability & Its Applications, Vol. 9, No. 3, 1964, pp. 497-500. doi:10.1137/1109069

[7] L. M. Viceira, “Testing for Structural Change in the Predictability of Asset Returns,” Manuscript, Harvard University, 1997.

[8] Y. Amihud and C. Hurvich, “Predictive Regression: A Reduced-Bias Estimation Method,” Journal of Financial and Quantitative Analysis, Vol. 39, No. 4, 2004, pp. 813-841. doi:10.1017/S0022109000003227

[9] J. Y. Park and S. B. Hahn, “Cointegrating Regressions with Time Varying Coefficients,” Econometric Theory, Vol. 15, 1999, pp. 664-703. doi:10.1017/S0266466699155026

[10] Y. Chang and E. Martinez-Chombo, “Electricity Demand Analysis Using Cointegration and Error-Correction Models with Time Varying Parameters: The Mexican Case,” Working Paper, Texas A. M. University, 2003.

[11] Z. Cai, Q. Li and J. Y. Park, “Functional-Coefficient Models for Nonstationary Time Series Data,” Journal of Econometrics, Vol. 2, 2006, pp. 101-113.

[12] G. Elliott and J. H. Stock, “Inference in Time Series Regression When the Order of Integration of a Regressor Is Unknown,” Econometric Theory, Vol. 10, No. 3-4, 1994, pp. 672-700. doi:10.1017/S0266466600008720

[13] C. L. Cavanagh, G. Elliott and J. H. Stock, “Inference in Models with Nearly Integrated Regressors,” Econometric Theory, Vol. 11, No. 5, 1995, pp. 1131-1147. doi:10.1017/S0266466600009981

[14] W. Torous, R. Valkanov and S. Yan, “On Predicting Stock Returns with Nearly Integrated Explanatory Variables,” Journal of Business, Vol. 77, No. 4, 2004, pp. 937-966. doi:10.1086/422634

[15] C. Polk, S. Thompson and T. Vuolteenaho, “Cross-Sectional Forecasts of the Equity Premium,” Journal of Financial Economics, Vol. 81, No. 1, 2006, pp. 101-141. doi:10.1016/j.jfineco.2005.03.013

[16] B. Rossi, “Expectation Hypothesis Tests and Predictive Regressions at Long Horizons,” Econometrics Journal, Vol. 10, No. 3, 2007, pp. 1-26. doi:10.1111/j.1368-423X.2007.00222.x

[17] M. Lettau and S. Ludvigsson, “Consumption, Aggregate Wealth, and Expected Stock Returns,” Journal of Finance, Vol. 56, No. 3, 2001, pp. 815-849. doi:10.1111/0022-1082.00347

[18] A. Goyal and I. Welch, “Predicting the Equity Premium with Dividend Ratios, Management Science, Vol. 49, No. 5, 2003, pp. 639-654. doi:10.1287/mnsc.49.5.639.15149

[19] A. Ang and G. Bekaert, “Stock Return Predictability: Is It There?” Review of Financial Studies, Vol. 20, No. 3, 2007, pp. 651-707. doi:10.1093/rfs/hhl021

[20] C. R. Nelson and M. J. Kim, “Predictable Stock Returns: The Role of Small Sample Bias,” Journal of Finance, Vol. 48, No. 2, 1993, pp. 641-661. doi:10.1111/j.1540-6261.1993.tb04731.x

[21] J. Lewellen, “Predicting Returns with Financial Ratios,” Journal of Financial Economics, Vol. 74, No. 2, 2004, pp. 209-235. doi:10.1016/j.jfineco.2002.11.002

[22] Z. Cai and Y. Wang, “Instability of Predictability of Asset Returns,” Working Paper, University of North Carolina at Charlotte, 2009.

[23] A. Torgovitsky, “Identification of Nonseparable Models with General Instruments,” Working Paper, Yale University, 2011.

[24] R. L. Matzkin, “Nonparametric Estimation of Nonadditive Random Functions,” Econometrica, Vol. 71, No. 5, 2003, pp. 1339-1375. doi:10.1111/1468-0262.00452

[1] N. G. Mankiw and M. Shapiro, “Do We Reject Too Often? Small Sample Properties of Tests of Rational Expectation models,” Economics Letters, Vol. 20, 1986, pp. 139-145.

[2] R. Stambaugh, “Bias in Regressions with Lagged Stochastic Regressors,” Working Paper, University of Chicago, 1986.

[3] J. Campbell and M. Yogo, “Efficient Tests of Stock Return Predictability,” Journal of Financial Econometrics, Vol. 81, No. 1, 2006, pp. 27-60. doi:10.1016/j.jfineco.2005.05.008

[4] B. S. Paye and A. Timmermann, “Instability of Return Prediction Models,” Journal of Empirical Finance, Vol. 13, No. 3, 2006, pp. 274-315. doi:10.1016/j.jempfin.2005.11.001

[5] T. Dangl and M. Halling, “Predictive Regressions with Time-Varying Coefficients,” Working Paper, School of Business, University of Utah, 2007.

[6] E. A. Nadaraya, “Some New Estimates for Distribution Functions,” Theory of Probability & Its Applications, Vol. 9, No. 3, 1964, pp. 497-500. doi:10.1137/1109069

[7] L. M. Viceira, “Testing for Structural Change in the Predictability of Asset Returns,” Manuscript, Harvard University, 1997.

[8] Y. Amihud and C. Hurvich, “Predictive Regression: A Reduced-Bias Estimation Method,” Journal of Financial and Quantitative Analysis, Vol. 39, No. 4, 2004, pp. 813-841. doi:10.1017/S0022109000003227

[9] J. Y. Park and S. B. Hahn, “Cointegrating Regressions with Time Varying Coefficients,” Econometric Theory, Vol. 15, 1999, pp. 664-703. doi:10.1017/S0266466699155026

[10] Y. Chang and E. Martinez-Chombo, “Electricity Demand Analysis Using Cointegration and Error-Correction Models with Time Varying Parameters: The Mexican Case,” Working Paper, Texas A. M. University, 2003.

[11] Z. Cai, Q. Li and J. Y. Park, “Functional-Coefficient Models for Nonstationary Time Series Data,” Journal of Econometrics, Vol. 2, 2006, pp. 101-113.

[12] G. Elliott and J. H. Stock, “Inference in Time Series Regression When the Order of Integration of a Regressor Is Unknown,” Econometric Theory, Vol. 10, No. 3-4, 1994, pp. 672-700. doi:10.1017/S0266466600008720

[13] C. L. Cavanagh, G. Elliott and J. H. Stock, “Inference in Models with Nearly Integrated Regressors,” Econometric Theory, Vol. 11, No. 5, 1995, pp. 1131-1147. doi:10.1017/S0266466600009981

[14] W. Torous, R. Valkanov and S. Yan, “On Predicting Stock Returns with Nearly Integrated Explanatory Variables,” Journal of Business, Vol. 77, No. 4, 2004, pp. 937-966. doi:10.1086/422634

[15] C. Polk, S. Thompson and T. Vuolteenaho, “Cross-Sectional Forecasts of the Equity Premium,” Journal of Financial Economics, Vol. 81, No. 1, 2006, pp. 101-141. doi:10.1016/j.jfineco.2005.03.013

[16] B. Rossi, “Expectation Hypothesis Tests and Predictive Regressions at Long Horizons,” Econometrics Journal, Vol. 10, No. 3, 2007, pp. 1-26. doi:10.1111/j.1368-423X.2007.00222.x

[17] M. Lettau and S. Ludvigsson, “Consumption, Aggregate Wealth, and Expected Stock Returns,” Journal of Finance, Vol. 56, No. 3, 2001, pp. 815-849. doi:10.1111/0022-1082.00347

[18] A. Goyal and I. Welch, “Predicting the Equity Premium with Dividend Ratios, Management Science, Vol. 49, No. 5, 2003, pp. 639-654. doi:10.1287/mnsc.49.5.639.15149

[19] A. Ang and G. Bekaert, “Stock Return Predictability: Is It There?” Review of Financial Studies, Vol. 20, No. 3, 2007, pp. 651-707. doi:10.1093/rfs/hhl021

[20] C. R. Nelson and M. J. Kim, “Predictable Stock Returns: The Role of Small Sample Bias,” Journal of Finance, Vol. 48, No. 2, 1993, pp. 641-661. doi:10.1111/j.1540-6261.1993.tb04731.x

[21] J. Lewellen, “Predicting Returns with Financial Ratios,” Journal of Financial Economics, Vol. 74, No. 2, 2004, pp. 209-235. doi:10.1016/j.jfineco.2002.11.002

[22] Z. Cai and Y. Wang, “Instability of Predictability of Asset Returns,” Working Paper, University of North Carolina at Charlotte, 2009.

[23] A. Torgovitsky, “Identification of Nonseparable Models with General Instruments,” Working Paper, Yale University, 2011.

[24] R. L. Matzkin, “Nonparametric Estimation of Nonadditive Random Functions,” Econometrica, Vol. 71, No. 5, 2003, pp. 1339-1375. doi:10.1111/1468-0262.00452