IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.20415.html

New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings

Author

Listed:
  • Luca Margaritella
  • Ovidijus Stauskas

Abstract

We provide the theoretical foundation for the recent tests of equal forecast accuracy and encompassing by Pitarakis (2023) and Pitarakis (2025), when the competing forecast specification is that of a factor-augmented regression model. This should be of interest for practitioners, as there is no theory justifying the use of these simple and powerful tests in such context. In pursuit of this, we employ a novel theory to incorporate the empirically well-documented fact of homogeneously/heterogeneously weak factor loadings, and track their effect on the forecast comparison problem.

Suggested Citation

  • Luca Margaritella & Ovidijus Stauskas, 2024. "New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings," Papers 2409.20415, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2409.20415
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2409.20415
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    2. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    3. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    4. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    5. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
    6. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    7. Matteo Barigozzi & Haeran Cho & Dom Owens, 2024. "FNETS: Factor-Adjusted Network Estimation and Forecasting for High-Dimensional Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 890-902, July.
    8. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    9. Yayi Yan & Tingting Cheng, 2022. "Factor-augmented forecasting regressions with threshold effects [What drives oil prices? Emerging versus developed economies]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 134-154.
    10. Todd Clark & Michael McCracken, 2012. "Reality Checks and Comparisons of Nested Predictive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 53-66.
    11. Sandra Eickmeier & Christina Ziegler, 2008. "How successful are dynamic factor models at forecasting output and inflation? A meta-analytic approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 237-265.
    12. 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.
    13. Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
    14. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    15. Yoshimasa Uematsu & Takashi Yamagata, 2022. "Inference in Sparsity-Induced Weak Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 126-139, December.
    16. Barbara Rossi, 2005. "Testing Long-Horizon Predictive Ability With High Persistence, And The Meese-Rogoff Puzzle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(1), pages 61-92, February.
    17. Mikolajun, Irena & Lodge, David, 2016. "Advanced economy inflation: the role of global factors," Working Paper Series 1948, European Central Bank.
    18. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    19. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    20. Peter Reinhard Hansen & Allan Timmermann, 2015. "Equivalence Between Out‐of‐Sample Forecast Comparisons and Wald Statistics," Econometrica, Econometric Society, vol. 83, pages 2485-2505, November.
    21. Pitarakis, Jean-Yves, 2025. "A Novel Approach To Predictive Accuracy Testing In Nested Environments," Econometric Theory, Cambridge University Press, vol. 41(1), pages 35-78, February.
    22. Tommaso Monacelli & Luca Sala, 2009. "The International Dimension of Inflation: Evidence from Disaggregated Consumer Price Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(s1), pages 101-120, February.
    23. Tom Boot & Bart Keijsers, 2025. "Diffusion index forecasts under weaker loadings: PCA, ridge regression, and random projections," Papers 2506.09575, arXiv.org.
    24. Gonçalves, Sílvia & McCracken, Michael W. & Perron, Benoit, 2017. "Tests of equal accuracy for nested models with estimated factors," Journal of Econometrics, Elsevier, vol. 198(2), pages 231-252.
    25. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    26. Jean-Yves Pitarakis, 2023. "Direct Multi-Step Forecast based Comparison of Nested Models via an Encompassing Test," Papers 2312.16099, arXiv.org.
    27. He, Yong & Li, Lingxiao & Liu, Dong & Zhou, Wen-Xin, 2025. "Huber Principal Component Analysis for large-dimensional factor models," Journal of Econometrics, Elsevier, vol. 249(PB).
    28. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    29. Christian Gillitzer & Martin McCarthy, 2019. "Does global inflation help forecast inflation in industrialized countries?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 850-857, August.
    30. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
    31. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    32. 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.
    33. Hong, Shengjie & Su, Liangjun & Wang, Yaqi, 2025. "Inference In Partially Identified Panel Data Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 41(3), pages 489-550, June.
    34. Hendry, David F. & Richard, Jean-Francois, 1982. "On the formulation of empirical models in dynamic econometrics," Journal of Econometrics, Elsevier, vol. 20(1), pages 3-33, October.
    35. 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.
    36. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    37. Jack Fosten, 2016. "Forecast evaluation with factor-augmented models," University of East Anglia School of Economics Working Paper Series 2016-05, School of Economics, University of East Anglia, Norwich, UK..
    38. 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.
    39. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, March.
    40. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2010. "Improved penalization for determining the number of factors in approximate factor models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1806-1813, December.
    41. Matteo Barigozzi & Marc Hallin, 2026. "The Dynamic, the Static, and the Weak: Factor Models and the Analysis of High‐Dimensional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(1), pages 201-219, January.
    42. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, July.
    43. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
    44. Ovidijus Stauskas & Joakim Westerlund, 2022. "Tests of Equal Forecasting Accuracy for Nested Models with Estimated CCE Factors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1745-1758, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Alessandro Morico & Ovidijus Stauskas, 2025. "Robust Tests for Factor-Augmented Regressions with an Application to the novel EA-MD-QD Dataset," Papers 2504.08455, arXiv.org, revised Nov 2025.
    2. Alessandro Morico & Ovidijus Stauskas, 2026. "Robust Tests of Forecast Accuracy for Factor‐Augmented Regressions With an Application to the Novel EA‐MD‐QD Dataset," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 41(5), pages 549-566, August.

    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. Alessandro Morico & Ovidijus Stauskas, 2025. "Robust Tests for Factor-Augmented Regressions with an Application to the novel EA-MD-QD Dataset," Papers 2504.08455, arXiv.org, revised Nov 2025.
    2. Alessandro Morico & Ovidijus Stauskas, 2026. "Robust Tests of Forecast Accuracy for Factor‐Augmented Regressions With an Application to the Novel EA‐MD‐QD Dataset," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 41(5), pages 549-566, August.
    3. Gonçalves, Sílvia & McCracken, Michael W. & Perron, Benoit, 2017. "Tests of equal accuracy for nested models with estimated factors," Journal of Econometrics, Elsevier, vol. 198(2), pages 231-252.
    4. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    5. Karen Miranda & Pilar Poncela & Esther Ruiz, 2022. "Dynamic factor models: Does the specification matter?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 397-428, May.
    6. Tom Boot & Bart Keijsers, 2025. "Diffusion index forecasts under weaker loadings: PCA, ridge regression, and random projections," Papers 2506.09575, arXiv.org.
    7. Matteo Barigozzi & Marc Hallin, 2026. "The Dynamic, the Static, and the Weak: Factor Models and the Analysis of High‐Dimensional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(1), pages 201-219, January.
    8. Peiyun Jiang & Yoshimasa Uematsu & Takashi Yamagata, 2025. "Bias Correction in Factor-Augmented Regression Models with Weak Factors," Papers 2509.02066, arXiv.org, revised Oct 2025.
    9. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2024. "Predictive ability tests with possibly overlapping models," Journal of Econometrics, Elsevier, vol. 241(1).
    10. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," ISER Discussion Paper 1053r, Institute of Social and Economic Research, The University of Osaka, revised Mar 2020.
    11. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    12. Tingting Cheng & Jiachen Cong & Fei Liu & Xuanbin Yang, 2025. "Binary Response Forecasting under a Factor-Augmented Framework," Papers 2507.16462, arXiv.org.
    13. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2020. "Estimation of large dimensional conditional factor models in finance," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 219-282, Elsevier.
    14. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org, revised Nov 2024.
    15. 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.
    16. Mario Forni & Alessandro Giovannelli & Marco Lippi & Stefano Soccorsi, 2018. "Dynamic factor model with infinite‐dimensional factor space: Forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 625-642, August.
    17. 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.
    18. Juho Koistinen & Bernd Funovits, 2022. "Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization," Papers 2202.00310, arXiv.org, revised Feb 2022.
    19. Wanbo Lu & Guanglin Huang & Kris Boudt, 2024. "Estimation of Non-Gaussian Factors Using Higher-order Multi-cumulants in Weak Factor Models," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 24/1085, Ghent University, Faculty of Economics and Business Administration.
    20. Masud Alam, 2024. "Output, employment, and price effects of U.S. narrative tax changes: a factor-augmented vector autoregression approach," Empirical Economics, Springer, vol. 67(4), pages 1421-1471, October.

    More about this item

    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:arx:papers:2409.20415. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.