IDEAS home Printed from https://ideas.repec.org/p/inu/caeprp/2022001.html
   My bibliography  Save this paper

A New Test for Multiple Predictive Regression

Author

Listed:
  • Ke-Li Xu

    (Department of Economics, Indiana University)

  • Junjie Guo

    (School of Finance, Central University of Finance and Economics, Beijing, China)

Abstract

We consider inference for predictive regressions with multiple predictors. Extant tests for predictability may perform unsatisfactorily and tend to discover spurious predictability as the number of predictors increases. We propose a battery of new instrumental-variables based tests which involve enforcement or partial enforcement of the null hypothesis in variance estimation. A test based on the few-predictors-at-a-time parsimonious system approach is recommended. Empirical Monte Carlos demonstrate the remarkable ?finite-sample performance regardless of numerosity of predictors and their persistence properties. Empirical application to equity premium predictability is provided.

Suggested Citation

  • Ke-Li Xu & Junjie Guo, 2021. "A New Test for Multiple Predictive Regression," CAEPR Working Papers 2022-001 Classification-C, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    • Handle: RePEc:inu:caeprp:2022001
    as

    Download full text from publisher

    File URL: https://caepr.indiana.edu/RePEc/inu/caeprp/caepr2022-001.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Martin Lettau & Stijn Van Nieuwerburgh, 2008. "Reconciling the Return Predictability Evidence," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1607-1652, July.
    2. Ai Deng, 2014. "Understanding Spurious Regression in Financial Economics," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 122-150.
    3. Willa W. Chen & Rohit S. Deo & Yanping Yi, 2013. "Uniform Inference in Predictive Regression Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 525-533, October.
    4. Yakov Amihud & Clifford M. Hurvich & Yi Wang, 2009. "Multiple-Predictor Regressions: Hypothesis Testing," Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 413-434, January.
    5. 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.
    6. Mete Kilic & Ivan Shaliastovich, 2019. "Good and Bad Variance Premia and Expected Returns," Management Science, INFORMS, vol. 67(6), pages 2522-2544, June.
    7. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
    8. John H. Cochrane, 2011. "Presidential Address: Discount Rates," Journal of Finance, American Finance Association, vol. 66(4), pages 1047-1108, August.
    9. 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.
    10. Hui Chen & Scott Joslin & Sophie Xiaoyan Ni, 2019. "Demand for Crash Insurance, Intermediary Constraints, and Risk Premia in Financial Markets," Review of Financial Studies, Society for Financial Studies, vol. 32(1), pages 228-265.
    11. Breitung, Jörg & Demetrescu, Matei, 2015. "Instrumental variable and variable addition based inference in predictive regressions," Journal of Econometrics, Elsevier, vol. 187(1), pages 358-375.
    12. Hjalmarsson, Erik, 2011. "New Methods for Inference in Long-Horizon Regressions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(3), pages 815-839, June.
    13. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    14. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2020. "The Pricing of Tail Risk and the Equity Premium: Evidence From International Option Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 662-678, July.
    15. John H. Cochrane, 2008. "The Dog That Did Not Bark: A Defense of Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1533-1575, July.
    16. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    17. A. Chudik & G. Kapetanios & M. Hashem Pesaran, 2018. "A One Covariate at a Time, Multiple Testing Approach to Variable Selection in High‐Dimensional Linear Regression Models," Econometrica, Econometric Society, vol. 86(4), pages 1479-1512, July.
    18. Hosseinkouchack, Mehdi & Demetrescu, Matei, 2021. "Finite-Sample Size Control Of Ivx-Based Tests In Predictive Regressions," Econometric Theory, Cambridge University Press, vol. 37(4), pages 769-793, August.
    19. Natalia Sizova, 2013. "Long-Horizon Return Regressions With Historical Volatility and Other Long-Memory Variables," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 546-559, October.
    20. Ľuboš Pástor & Robert F. Stambaugh, 2009. "Predictive Systems: Living with Imperfect Predictors," Journal of Finance, American Finance Association, vol. 64(4), pages 1583-1628, August.
    21. 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.
    22. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
    23. David E. Rapach & Jack K. Strauss & Guofu Zhou, 2013. "International Stock Return Predictability: What Is the Role of the United States?," Journal of Finance, American Finance Association, vol. 68(4), pages 1633-1662, August.
    24. Markku Lanne, 2002. "Testing The Predictability Of Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 407-415, August.
    25. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    26. Hui Chen & Scott Joslin & Sophie X. Ni, 2019. "Demand for Crash Insurance, Intermediary Constraints, and Risk Premia in Financial Markets," NBER Working Papers 25573, National Bureau of Economic Research, Inc.
    27. Peter C. B. Phillips, 2015. "Pitfalls and Possibilities in Predictive Regression," Cowles Foundation Discussion Papers 2003, Cowles Foundation for Research in Economics, Yale University.
    28. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    29. Daniela Osterrieder & Daniel Ventosa-Santaulària & J Eduardo Vera-Valdés, 2019. "The VIX, the Variance Premium, and Expected Returns," Journal of Financial Econometrics, Oxford University Press, vol. 17(4), pages 517-558.
    30. Alexandros Kostakis & Tassos Magdalinos & Michalis P. Stamatogiannis, 2015. "Robust Econometric Inference for Stock Return Predictability," Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1506-1553.
    31. Eaton, Gregory W. & Paye, Bradley S., 2017. "Payout Yields and Stock Return Predictability: How Important Is the Measure of Cash Flow?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(4), pages 1639-1666, August.
    Full references (including those not matched with items on IDEAS)

    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. Demetrescu, Matei & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2023. "Transformed regression-based long-horizon predictability tests," Journal of Econometrics, Elsevier, vol. 237(2).
    2. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    3. Demetrescu, Matei & Georgiev, Iliyan & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2022. "Testing for episodic predictability in stock returns," Journal of Econometrics, Elsevier, vol. 227(1), pages 85-113.
    4. Demetrescu, Matei & Rodrigues, Paulo M.M., 2022. "Residual-augmented IVX predictive regression," Journal of Econometrics, Elsevier, vol. 227(2), pages 429-460.
    5. Zongwu Cai & Haiqiang Chen & Xiaosai Liao, 2020. "A New Robust Inference for Predictive Quantile Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202002, University of Kansas, Department of Economics, revised Feb 2020.
    6. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2021. "Simple tests for stock return predictability with good size and power properties," Journal of Econometrics, Elsevier, vol. 224(1), pages 198-214.
    7. Zongwu Cai & Seong Yeon Chang, 2018. "A New Test In A Predictive Regression with Structural Breaks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201811, University of Kansas, Department of Economics, revised Dec 2018.
    8. Cai, Zongwu & Chen, Haiqiang & Liao, Xiaosai, 2023. "A new robust inference for predictive quantile regression," Journal of Econometrics, Elsevier, vol. 234(1), pages 227-250.
    9. Chevillon, Guillaume, 2017. "Robustness of Multistep Forecasts and Predictive Regressions at Intermediate and Long Horizons," ESSEC Working Papers WP1710, ESSEC Research Center, ESSEC Business School.
    10. Rapach, David & Zhou, Guofu, 2013. "Forecasting Stock Returns," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 328-383, Elsevier.
    11. Daniela Osterrieder & Daniel Ventosa-Santaulària & J. Eduardo Vera-Valdés, 2015. "Unbalanced Regressions and the Predictive Equation," CREATES Research Papers 2015-09, Department of Economics and Business Economics, Aarhus University.
    12. Andersen, Torben G. & Varneskov, Rasmus T., 2022. "Testing for parameter instability and structural change in persistent predictive regressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 361-386.
    13. Charles, Amélie & Darné, Olivier & Kim, Jae H., 2017. "International stock return predictability: Evidence from new statistical tests," International Review of Financial Analysis, Elsevier, vol. 54(C), pages 97-113.
    14. Bingduo Yang & Xiaohui Liu & Liang Peng & Zongwu Cai, 2018. "Unified Tests for a Dynamic Predictive Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201808, University of Kansas, Department of Economics, revised Sep 2018.
    15. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2019. "Predictive Regressions," UC3M Working papers. Economics 28554, Universidad Carlos III de Madrid. Departamento de Economía.
    16. Victoria Atanasov & Stig V. Møller & Richard Priestley, 2020. "Consumption Fluctuations and Expected Returns," Journal of Finance, American Finance Association, vol. 75(3), pages 1677-1713, June.
    17. Bakshi, Gurdip & Panayotov, George & Skoulakis, Georgios, 2011. "Improving the predictability of real economic activity and asset returns with forward variances inferred from option portfolios," Journal of Financial Economics, Elsevier, vol. 100(3), pages 475-495, June.
    18. Westerlund, Joakim & Narayan, Paresh, 2016. "Testing for predictability in panels of any time series dimension," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1162-1177.
    19. Avdis, Efstathios & Wachter, Jessica A., 2017. "Maximum likelihood estimation of the equity premium," Journal of Financial Economics, Elsevier, vol. 125(3), pages 589-609.
    20. Lawrenz, Jochen & Zorn, Josef, 2017. "Predicting international stock returns with conditional price-to-fundamental ratios," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 159-184.

    More about this item

    Keywords

    Curse of dimensionality; Lagrange-multipliers test; persistence; predictive regression; return predictability;
    All these keywords.

    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:inu:caeprp:2022001. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Center for Applied Economics and Policy Research (email available below). General contact details of provider: https://edirc.repec.org/data/caeprus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.