Lee, JiHyung (2015): Predictive quantile regression with persistent covariates: IVXQR approach. Forthcoming in: Journal of Econometrics

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Abstract
This paper develops econometric methods for inference and prediction in quantile regression (QR) allowing for persistent predictors. Conventional QR econometric techniques lose their validity when predictors are highly persistent. I adopt and extend a methodology called IVX filtering (Magdalinos and Phillips, 2009) that is designed to handle predictor variables with various degrees of persistence. The proposed IVXQR methods correct the distortion arising from persistent multivariate predictors while preserving discriminatory power. Simulations confirm that IVXQR methods inherit the robust properties of QR. These methods are employed to examine the predictability of US stock returns at various quantile levels.
Item Type:  MPRA Paper 

Original Title:  Predictive quantile regression with persistent covariates: IVXQR approach 
Language:  English 
Keywords:  IVX filtering, Local to unity, Multivariate predictors, Predictive regression, Quantile regression. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  65150 
Depositing User:  JiHyung Lee 
Date Deposited:  21 Jun 2015 03:50 
Last Modified:  27 Sep 2019 12:26 
References:  Bickel, P.J, 1975, OneStep Huber Estimates in the Linear Model. Journal of the American Statistical Association, 70(350), pp.428434. Campbell, J. and S. Thompson, 2008, Predicting excess stock returns out of sample: can anything beat the historical average?. Review of Financial Studies, 21(4), pp. 15091531. Campbell, J. and M. Yogo, 2006, Efficient tests of stock return predictability. Journal of Financial Economics, 81(1), 2760. Cavanagh, C., G. Elliott. and J.Stock, 1995, Inference in models with nearly integrated regressors. Econometric Theory, 11(05), 11311147. Cenesizoglu, T and A. Timmermann, 2008, Is the distribution of stock returns predictable?. Unpublished Manuscript, HEC Montreal and UCSD. Chernozhukov, V, 2005, Extremal quantile regression. Annals of Statistics, 33, 806839. Chernozhukov, V. and I. FernandezVal, 2011, Inference for extremal conditional quantile models, with an application to market and birthweight risks. Review of Economic Studies, 78(2), 559589. Davis, R. A., & Mikosch, T, 2009, The extremogram: a correlogram for extreme events. Bernoulli, 15(4), 9771009. Elliott, G. and J.H. Stock, 1994, Inference in time series regression when the order of integration of a regressor is unknown. Econometric Theory, 10(34), 672700. Fama, E. and K. French, 1993, Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 356. Gonzalo, J., & Pitarakis, J. Y., 2012, Regimespecific predictability in predictive regressions. Journal of Business & Economic Statistics, 30(2), 229241. Goyal, A and I. Welch, 2008, A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies, 21(4), 14551508. Han, H., Linton, O., Oka, T., & Whang, Y. J., 2014, The crossquantilogram: measuring quantile dependence and testing directional predictability between time series. Available at SSRN 2338468. Jansson, M. and M. Moreira, 2006, Optimal inference in regression models with nearly integrated regressors. Econometrica, 74(3), 681714. Knight, K, 1989, Limit theory for autoregressiveparameter estimates in an infinitevariance random walk. Canadian Journal of Statistics, 17, 261278. Koenker, R, 2005, Econometric Society Monographs: Quantile Regression. Cambridge Press. Koenker, R and G. Basset, 1978, Regression quantiles. Econometrica 46, 3349. Kostakis, A., Magdalinos, T., & Stamatogiannis, M. P., 2014, Robust econometric inference for stock return predictability. Review of Financial Studies, hhu139. Lee, J.H., 2014, Online Supplement to "Predictive Quantile Regression with Persistent Covariates: IVXQR Approach". Available at https://sites.google.com/site/jihyung412/research. Linton, O., & Whang, Y. J., 2007, The quantilogram: With an application to evaluating directional predictability. Journal of Econometrics, 141(1), 250282. Magdalinos, T. and P. C. B Phillips, 2009, Econometric inference in the vicinity of unity. CoFie Working Paper (7), Singapore Management University. Maynard A., K. Shimotsu and Y. Wang, 2011, Inference in predictive quantile regressions. Unpublished Manuscript. Mikusheva, A., 2007, Uniform inference in autoregressive models. Econometrica, 75(5), 14111452. Pakes, A. and D. Pollard, 1989, Simulation and the asymptotics of optimization estimators. Econometrica 57(5), pp.10271057. Phillips, P. C. B., 1995, Fully modified least squares and vector autoregression. Econometrica 63(5), 10231078. Phillips, P. C. B., 2014, On confidence Intervals for autoregressive roots and predictive regression. Econometrica, 82(3), 11771195. Phillips, P. C. B., 1989, Partially identified econometric models. Econometric Theory, 5(2), pp. 181240 Phillips, P. C. B., 1987, Towards a unified asymptotic theory for autoregression. Biometrika 74, 535547 Phillips, P. C. B. and B. Hansen, 1990, Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies, 57(1), 99. Phillips, P. C. B and J.H. Lee, 2013, Predictive regression under various degrees of persistence and robust longhorizon regression. Journal of Econometrics, 177, 250264. Phillips, P. C. B and J.H. Lee, 2014, Robust econometric inference with mixed integrated and mildly explosive regressors. Unpublished Manuscript. Phillips, P. C. B. and T. Magdalinos, 2007, Limit theory for moderate deviations from a unit root. Journal of Econometrics 136, 115130. Phillips, P. C. B. and V. Solo, 1992, Asymptotics for linear processes. The Annals of Statistics, pp. 9711001. Pollard, D., 1991, Asymptotics for least absolute deviation regression estimators. Econometric Theory, 7(2), pp. 186199. Stock, J., 1991, Confidence intervals for the largest autoregressive root in US macroeconomic time series. Journal of Monetary Economics, 28(3), 435459. Xiao, Z., 2009, Quantile cointegrating regression. Journal of Econometrics, 150, 248260. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/65150 