IDEAS home Printed from https://ideas.repec.org/p/ucy/cypeua/14-2012.html
   My bibliography  Save this paper

Nonparametric Predictive Regression

Author

Listed:
  • Ioannis Kasparis
  • Elena Andreou
  • Peter C. B. Phillips

Abstract

A unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The test statistics are related to those of Kasparis and Phillips (2012) and are obtained by kernel regression. The limit distribution of these predictive tests holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. In this sense the proposed tests provide a unifying framework for predictive inference, allowing for possibly nonlinear relationships of unknown form, and offering robustness to integration order and functional form. Under the null of no predictability the limit distributions of the tests involve functionals of independent ÷² variates. The tests are consistent and divergence rates are faster when the predictor is stationary. Asymptotic theory and simulations show that the proposed tests are more powerful than existing parametric predictability tests when deviations from unity are large or the predictive regression is nonlinear. Some empirical illustrations to monthly SP500 stock returns data are provided.

Suggested Citation

  • Ioannis Kasparis & Elena Andreou & Peter C. B. Phillips, 2012. "Nonparametric Predictive Regression," University of Cyprus Working Papers in Economics 14-2012, University of Cyprus Department of Economics.
  • Handle: RePEc:ucy:cypeua:14-2012
    as

    Download full text from publisher

    File URL: http://papers.econ.ucy.ac.cy/RePEc/papers/14-12.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
    2. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    3. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    4. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    5. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    6. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    8. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    9. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    10. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    11. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    12. P. M. Robinson & J. Hualde, 2003. "Cointegration in Fractional Systems with Unknown Integration Orders," Econometrica, Econometric Society, vol. 71(6), pages 1727-1766, November.
    13. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1373-1403, October.
    14. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    15. Markku Lanne, 2002. "Testing The Predictability Of Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 407-415, August.
    16. Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-222, April.
    17. Walter Torous & Rossen Valkanov & Shu Yan, 2004. "On Predicting Stock Returns with Nearly Integrated Explanatory Variables," The Journal of Business, University of Chicago Press, vol. 77(4), pages 937-966, October.
    18. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    19. Robinson, Peter M. & Hualde, Javier, 2003. "Cointegration in fractional systems with unknown integration orders," LSE Research Online Documents on Economics 2223, London School of Economics and Political Science, LSE Library.
    20. Berkes, István & Horváth, Lajos, 2006. "Convergence Of Integral Functionals Of Stochastic Processes," Econometric Theory, Cambridge University Press, vol. 22(2), pages 304-322, April.
    21. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    22. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    23. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
    24. de Jong, R.M. & Bierens, H.J., 1994. "On the Limit Behavior of a Chi-Square Type Test if the Number of Conditional Moments Tested Approaches Infinity," Econometric Theory, Cambridge University Press, vol. 10(1), pages 70-90, March.
    25. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    26. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    27. Peter C. B. Phillips, 2014. "On Confidence Intervals for Autoregressive Roots and Predictive Regression," Econometrica, Econometric Society, vol. 82(3), pages 1177-1195, May.
    28. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    29. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    30. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    31. Berenguer Rico, Vanessa & Gonzalo, Jesús, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," UC3M Working papers. Economics we1115, Universidad Carlos III de Madrid. Departamento de Economía.
    32. Berenguer-Rico, Vanessa & Gonzalo, Jesús, 2014. "Summability of stochastic processes—A generalization of integration for non-linear processes," Journal of Econometrics, Elsevier, vol. 178(P2), pages 331-341.
    33. Wang, Qiying & Phillips, Peter C.B., 2011. "Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications," Econometric Theory, Cambridge University Press, vol. 27(2), pages 235-259, April.
    34. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
    35. repec:taf:jnlbes:v:30:y:2012:i:2:p:229-241 is not listed on IDEAS
    36. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    37. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    38. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
    39. Wang, Qiying, 2014. "Martingale Limit Theorem Revisited And Nonlinear Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 30(3), pages 509-535, June.
    40. Francesc Marmol & Carlos Velasco, 2004. "Consistent Testing of Cointegrating Relationships," Econometrica, Econometric Society, vol. 72(6), pages 1809-1844, November.
    41. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
    42. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Qiying & Wu, Dongsheng & Zhu, Ke, 2018. "Model checks for nonlinear cointegrating regression," Journal of Econometrics, Elsevier, vol. 207(2), pages 261-284.
    2. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    3. Biqing Cai & Jiti Gao, 2017. "A simple nonlinear predictive model for stock returns," Monash Econometrics and Business Statistics Working Papers 18/17, Monash University, Department of Econometrics and Business Statistics.
    4. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    5. Jean-Yves Pitarakis, 2017. "A Simple Approach for Diagnosing Instabilities in Predictive Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 851-874, October.
    6. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    7. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    8. Weilun Zhou & Jiti Gao & David Harris & Hsein Kew, 2019. "Semiparametric Single-index Predictive Regression," Monash Econometrics and Business Statistics Working Papers 25/19, Monash University, Department of Econometrics and Business Statistics.
    9. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2019. "Predictive Regressions," UC3M Working papers. Economics 28554, Universidad Carlos III de Madrid. Departamento de Economía.
    10. Devpura, Neluka & Narayan, Paresh Kumar & Sharma, Susan Sunila, 2018. "Is stock return predictability time-varying?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 52(C), pages 152-172.
    11. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.
    12. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
    13. Liu, Xiaohui & Yang, Bingduo & Cai, Zongwu & Peng, Liang, 2019. "A unified test for predictability of asset returns regardless of properties of predicting variables," Journal of Econometrics, Elsevier, vol. 208(1), pages 141-159.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.
    2. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    3. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    4. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    5. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    6. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    7. Biqing Cai & Jiti Gao & Dag Tjøstheim, 2017. "A New Class of Bivariate Threshold Cointegration Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 288-305, April.
    8. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    9. Erik Hjalmarsson, 2006. "Inference in Long-Horizon Regressions," International Finance Discussion Papers 853, Board of Governors of the Federal Reserve System (U.S.).
    10. Hjalmarsson, Erik, 2005. "On the Predictability of Global Stock Returns," Working Papers in Economics 161, University of Gothenburg, Department of Economics.
    11. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(1), pages 63-116, February.
    12. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.
    13. Lee, Ji Hyung, 2016. "Predictive quantile regression with persistent covariates: IVX-QR approach," Journal of Econometrics, Elsevier, vol. 192(1), pages 105-118.
    14. Nikitas Pittis & Christina Christou & Sarantis Kalyvitis & Christis Hassapis, 2009. "Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate," Review of International Economics, Wiley Blackwell, vol. 17(1), pages 144-155, February.
    15. Biqing Cai & Chaohua Dong & Jiti Gao, 2015. "Orthogonal Series Estimation in Nonlinear Cointegrating Models with Endogeneity," Monash Econometrics and Business Statistics Working Papers 18/15, Monash University, Department of Econometrics and Business Statistics.
    16. Jean-Yves Pitarakis, 2017. "A Simple Approach for Diagnosing Instabilities in Predictive Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 851-874, October.
    17. Jiti Gao & Peter C.B. Phillips, 2011. "Semiparametric Estimation in Multivariate Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 17/11, Monash University, Department of Econometrics and Business Statistics.
    18. Berenguer Rico, Vanessa & Gonzalo, Jesús, 2013. "Co-summability from linear to non-linear cointegration," UC3M Working papers. Economics we1312, Universidad Carlos III de Madrid. Departamento de Economía.
    19. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
    20. Biqing Cai & Jiti Gao, 2013. "Hermite Series Estimation in Nonlinear Cointegrating Models," Monash Econometrics and Business Statistics Working Papers 17/13, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Functional regression; Nonparametric predictability test; Nonparametric regression; Stock returns; Predictive regression;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ucy:cypeua:14-2012. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.ucy.ac.cy/econ/en .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.