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The three-pass regression filter: A new approach to forecasting using many predictors

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  • Kelly, Bryan
  • Pruitt, Seth

Abstract

We forecast a single time series using many predictor variables with a new estimator called the three-pass regression filter (3PRF). It is calculated in closed form and conveniently represented as a set of ordinary least squares regressions. 3PRF forecasts are consistent for the infeasible best forecast when both the time dimension and cross section dimension become large. This requires specifying only the number of relevant factors driving the forecast target, regardless of the total number of common factors driving the cross section of predictors. The 3PRF is a constrained least squares estimator and reduces to partial least squares as a special case. Simulation evidence confirms the 3PRF’s forecasting performance relative to alternatives. We explore two empirical applications: Forecasting macroeconomic aggregates with a large panel of economic indices, and forecasting stock market returns with price–dividend ratios of stock portfolios.

Suggested Citation

  • Kelly, Bryan & Pruitt, Seth, 2015. "The three-pass regression filter: A new approach to forecasting using many predictors," Journal of Econometrics, Elsevier, vol. 186(2), pages 294-316.
  • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:294-316
    DOI: 10.1016/j.jeconom.2015.02.011
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    Cited by:

    1. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
    2. Hyeongwoo Kim & Kyunghwan Ko, 2017. "Improving Forecast Accuracy of Financial Vulnerability: Partial Least Squares Factor Model Approach," Working Papers 2017-14, Economic Research Institute, Bank of Korea.
    3. Gupta, Rangan & Hammoudeh, Shawkat & Modise, Mampho P. & Nguyen, Duc Khuong, 2014. "Can economic uncertainty, financial stress and consumer sentiments predict U.S. equity premium?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 33(C), pages 367-378.
    4. repec:eee:finmar:v:38:y:2018:i:c:p:103-123 is not listed on IDEAS
    5. Stefano Giglio & Dacheng Xiu, 2017. "Inference on Risk Premia in the Presence of Omitted Factors," NBER Working Papers 23527, National Bureau of Economic Research, Inc.
    6. Liya Chu & Xue-Zhong He & Kai Li & Jun Tu, 2015. "Market Sentiment and Paradigm Shifts," Research Paper Series 356, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. repec:eee:eneeco:v:70:y:2018:i:c:p:472-483 is not listed on IDEAS
    8. repec:eee:econom:v:201:y:2017:i:2:p:292-306 is not listed on IDEAS
    9. Rodríguez, Julio & Poncela, Pilar & Fuentes, Julieta, 2014. "Selecting and combining experts from survey forecasts," DES - Working Papers. Statistics and Econometrics. WS ws140905, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Pierre Guerin & Danilo Leiva-Leon & Massimiliano Marcellino, 2016. "Markov-Switching Three-Pass Regression Filter," Working Papers 591, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    11. Grover, Sean P. & McCracken, Michael W., 2014. "Factor-based prediction of industry-wide bank stress," Review, Federal Reserve Bank of St. Louis, vol. 96(2), pages 173-194.
    12. Grover, Sean P. & Kliesen, Kevin L. & McCracken, Michael W., 2016. "A Macroeconomic News Index for Constructing Nowcasts of U.S. Real Gross Domestic Product Growth," Review, Federal Reserve Bank of St. Louis, vol. 98(4), pages 277-296.
    13. repec:ipg:wpaper:2013-020 is not listed on IDEAS
    14. Chen, Jian & Jiang, Fuwei & Li, Hongyi & Xu, Weidong, 2016. "Chinese stock market volatility and the role of U.S. economic variables," Pacific-Basin Finance Journal, Elsevier, vol. 39(C), pages 70-83.
    15. repec:kap:fmktpm:v:32:y:2018:i:1:d:10.1007_s11408-017-0302-3 is not listed on IDEAS
    16. Antoine A. Djogbenou, 2017. "Model Selection in Factor-Augmented Regressions with Estimated Factors," Working Papers 1391, Queen's University, Department of Economics.
    17. repec:eee:empfin:v:45:y:2018:i:c:p:126-140 is not listed on IDEAS
    18. Alessandro Barbarino & Efstathia Bura, 2017. "A Unified Framework for Dimension Reduction in Forecasting," Finance and Economics Discussion Series 2017-004, Board of Governors of the Federal Reserve System (U.S.).
    19. Giglio, Stefano & Kelly, Bryan & Pruitt, Seth, 2016. "Systemic risk and the macroeconomy: An empirical evaluation," Journal of Financial Economics, Elsevier, vol. 119(3), pages 457-471.
    20. repec:eee:ecmode:v:68:y:2018:i:c:p:644-660 is not listed on IDEAS
    21. Duo Qin & Qingchao Wang, 2016. "Predictive Macro-Impacts of PLS-based Financial Conditions Indices: An Application to the USA," Working Papers 201, Department of Economics, SOAS, University of London, UK.

    More about this item

    Keywords

    Forecast; Factor model; Principal components; Constrained least squares; Partial least squares;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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