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Bootstrap prediction intervals for factor models

Author

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  • Silvia 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, Bai and Ng (2006) proposed the construction of asymptotic intervals 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 OLS estimator as shown in a recent paper by Gonçalves and Perron (2014).

Suggested Citation

  • Silvia Gonçalves & Benoit Perron & Antoine Djogbenou, 2016. "Bootstrap prediction intervals for factor models," CIRANO Working Papers 2016s-19, CIRANO.
    • Handle: RePEc:cir:cirwor:2016s-19
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    1. Antoine Djogbenou & Silvia Gonçalves & Benoit Perron, 2015. "Bootstrap inference in regressions with estimated factors and serial correlation," CIRANO Working Papers 2015s-20, CIRANO.
    2. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    3. 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.
    4. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    5. 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.
    6. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    7. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    8. 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.
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    Citations

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    Cited by:

    1. Allayioti, Anastasia & Venditti, Fabrizio, 2024. "The role of comovement and time-varying dynamics in forecasting commodity prices," Working Paper Series 2901, European Central Bank.
    2. Gloria González‐Rivera & C. Vladimir Rodríguez‐Caballero & Esther Ruiz, 2024. "Expecting the unexpected: Stressed scenarios for economic growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 926-942, August.
    3. 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.
    4. Antoine Djogbenou & Silvia Gonçalves & Benoit Perron, 2015. "Bootstrap inference in regressions with estimated factors and serial correlation," CIRANO Working Papers 2015s-20, CIRANO.
    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. Gonçalves, Sílvia & Perron, Benoit, 2020. "Bootstrapping factor models with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 218(2), pages 476-495.
    7. 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.
    8. 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.
    9. Yohei Yamamoto & Naoko Hara, 2022. "Identifying factor‐augmented vector autoregression models via changes in shock variances," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(4), pages 722-745, June.
    10. Javier Maldonado & Esther Ruiz, 2021. "Accurate Confidence Regions for Principal Components Factors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(6), pages 1432-1453, December.
    11. 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.
    12. 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.
    13. Hande Karabiyik & Joakim Westerlund, 2021. "Forecasting using cross-section average–augmented time series regressions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 315-333.
    14. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    15. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.
    16. Diego Fresoli & Pilar Poncela & Esther Ruiz, 2024. "Dealing with idiosyncratic cross-correlation when constructing confidence regions for PC factors," Papers 2407.06883, arXiv.org.
    17. 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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    More about this item

    Keywords

    factor model; bootstrap; forecast; conditional mean;
    All these keywords.

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