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Bootstrap Prediction Intervals for Factor Models

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  • Sílvia Gonçalves
  • Benoit Perron
  • Antoine Djogbenou

Abstract

We propose bootstrap prediction intervals for an observation h periods into the future and its conditional mean. We assume that these forecasts are made using a set of factors extracted from a large panel of variables. Because we treat these factors as latent, our forecasts depend both on estimated factors and estimated regression coefficients. Under regularity conditions, asymptotic intervals have been shown to be valid under Gaussianity of the innovations. The bootstrap allows us to relax this assumption and to construct valid prediction intervals under more general conditions. Moreover, even under Gaussianity, the bootstrap leads to more accurate intervals in cases where the cross-sectional dimension is relatively small as it reduces the bias of the ordinary least-squares (OLS) estimator.

Suggested Citation

  • Sílvia Gonçalves & Benoit Perron & Antoine Djogbenou, 2017. "Bootstrap Prediction Intervals for Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 53-69, January.
  • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:1:p:53-69
    DOI: 10.1080/07350015.2015.1054492
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    1. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    2. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    3. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    4. Pan, Li & Politis, Dimitris N, 2014. "Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions," University of California at San Diego, Economics Working Paper Series qt67h5s74t, Department of Economics, UC San Diego.
    5. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    6. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    7. Antoine Djogbenou & Silvia Gonçalves & Benoit Perron, 2015. "Bootstrap inference in regressions with estimated factors and serial correlation," CIRANO Working Papers 2015s-20, CIRANO.
    8. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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    Cited by:

    1. GONÇALVES, Sílvia & PERRON, Benoit, 2018. "Bootstrapping factor models with cross sectional dependence," Cahiers de recherche 2018-07, Universite de Montreal, Departement de sciences economiques.
    2. Gonçalves, Sílvia & Perron, Benoit, 2020. "Bootstrapping factor models with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 218(2), pages 476-495.
    3. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Antoine Djogbenou & Sílvia Gonçalves & Benoit Perron, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 481-502, May.
    4. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    5. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    6. Cheng, Tingting & Gao, Jiti & Yan, Yayi, 2019. "Regime switching panel data models with interactive fixed effects," Economics Letters, Elsevier, vol. 177(C), pages 47-51.
    7. Antoine Djogbenou & Silvia Gonçalves & Benoit Perron, 2015. "Bootstrap inference in regressions with estimated factors and serial correlation," CIRANO Working Papers 2015s-20, CIRANO.
    8. Knut Are Aastveit & Claudia Foroni & Francesco Ravazzolo, 2017. "Density Forecasts With Midas Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 783-801, June.
    9. Min Seong Kim, 2021. "Robust Inference for Diffusion-Index Forecasts with Cross-Sectionally Dependent Data," Working papers 2021-04, University of Connecticut, Department of Economics.
    10. YAMAMOTO, Yohei, 2018. "Identifying Factor-Augmented Vector Autoregression Models via Changes in Shock Variances," Discussion paper series HIAS-E-72, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    11. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2019. "Density Forecasting," BEMPS - Bozen Economics & Management Paper Series BEMPS59, Faculty of Economics and Management at the Free University of Bozen.

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