IDEAS home Printed from
   My bibliography  Save this paper

In-sample inference and forecasting in misspecified factor models




This paper considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension reduction devices: principal components, Ridge, Landweber Fridman, and Partial Least Squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning parameter to be selected, we also propose data-driven selection methods based on cross- validation and establish their optimality. Monte Carlo simulations and an empirical application to forecasting inflation and output growth in the U.S. show that data-reduction methods out- perform conventional methods in several relevant settings, and might effectively guard against instabilities in predictors' forecasting ability.

Suggested Citation

  • Marine Carrasco & Barbara Rossi, 2016. "In-sample inference and forecasting in misspecified factor models," Economics Working Papers 1530, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1530

    Download full text from publisher

    File URL:
    File Function: Whole Paper
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, pages 365-411.
    2. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    5. Jan J. J. Groen & George Kapetanios, 2013. "Model Selection Criteria for Factor-Augmented Regressions-super-," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(1), pages 37-63, February.
    6. Inoue, Atsushi & Kilian, Lutz, 2008. "How Useful Is Bagging in Forecasting Economic Time Series? A Case Study of U.S. Consumer Price Inflation," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 511-522, June.
    7. Gonçalves, Sílvia & McCracken, Michael W. & Perron, Benoit, 2017. "Tests of equal accuracy for nested models with estimated factors," Journal of Econometrics, Elsevier, pages 231-252.
    8. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, pages 509-548.
    9. Huiyu Huang & Tae-Hwy Lee, 2010. "To Combine Forecasts or to Combine Information?," Econometric Reviews, Taylor & Francis Journals, vol. 29(5-6), pages 534-570.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Rossi, Barbara & Sekhposyan, Tatevik, 2014. "Evaluating predictive densities of US output growth and inflation in a large macroeconomic data set," International Journal of Forecasting, Elsevier, vol. 30(3), pages 662-682.
    12. Groen, Jan J.J. & Kapetanios, George, 2016. "Revisiting useful approaches to data-rich macroeconomic forecasting," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 221-239.
    13. Jonathan H. Wright, 2009. "Forecasting US inflation by Bayesian model averaging," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 131-144.
    14. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
    15. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    16. Julieta Fuentes & Pilar Poncela & Julio Rodríguez, 2015. "Sparse Partial Least Squares in Time Series for Macroeconomic Forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 576-595, June.
    17. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    18. Tommaso Proietti, 2016. "On the Selection of Common Factors for Macroeconomic Forecasting," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 593-628 Emerald Publishing Ltd.
    19. James H. Stock & Mark W. Watson, 2012. "Generalized Shrinkage Methods for Forecasting Using Many Predictors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 481-493, June.
    20. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    21. Brown, Stephen J, 1989. " The Number of Factors in Security Returns," Journal of Finance, American Finance Association, vol. 44(5), pages 1247-1262, December.
    22. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    23. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    24. 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.
    25. Mario Forni & Alessandro Giovannelli & Marco Lippi & Stefano Soccorsi, 2016. "Dynamic Factor Model with Infinite Dimensional Factor Space: Forecasting," Working Papers ECARES ECARES 2016-16, ULB -- Universite Libre de Bruxelles.
    26. Mao Takongmo, Charles Olivier & Stevanovic, Dalibor, 2015. "Selection Of The Number Of Factors In Presence Of Structural Instability: A Monte Carlo Study," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 177-233, Mars-Juin.
    27. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, pages 507-537.
    28. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    29. Jianqing Fan & Jinchi Lv & Lei Qi, 2011. "Sparse High-Dimensional Models in Economics," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 291-317, September.
    30. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(02), pages 260-284, April.
    31. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    32. Antoine A. Djogbenou, 2017. "Model Selection in Factor-Augmented Regressions with Estimated Factors," Working Papers 1391, Queen's University, Department of Economics.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank, Research Department.
    2. Smeekes, Stephan & Wijler, Etiënne, 2016. "Macroeconomic Forecasting Using Penalized Regression Methods," Research Memorandum 039, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. repec:aea:jecper:v:31:y:2017:i:2:p:59-86 is not listed on IDEAS
    4. Antoine A. Djogbenou, 2017. "Model Selection in Factor-Augmented Regressions with Estimated Factors," Working Papers 1391, Queen's University, Department of Economics.

    More about this item


    Forecasting; regularization methods; factor models; Ridge; partial least squares; principal components; sparsity; large datasets; variable selection; GDP forecasts; inflation forecasts;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:upf:upfgen:1530. 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: .

    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.