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Testing for Structural Stability of Factor Augmented Forecasting Models

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  • Valentina Corradi

    () (Warwick University)

  • Norman Swanson

    () (Rutgers University)

Abstract

Mild factor loading instability, particularly if sufficiently independent across the different constituent variables, does not affect the estimation of the number of factors, nor subsequent estimation of the factors themselves (see e.g. Stock and Watson (2009)). This result does not hold in the presence of large common breaks in the factor loadings, however. In this case, information criteria overestimate the number of breaks. Additionally, estimated factors are no longer consistent estimators of "true" factors. Hence, various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings. One reason why this is a positive development is that in applied work, factor augmented forecasting models are used widely for prediction, and it is important to understand when such models are stable. Now, forecast failure of factor augmented models can be due to either factor loading instability, regression coefficient instability, or both. To address this issue, we develop a test for the joint hypothesis of structural stability of both factor loadings and factor augmented forecasting model regression coefficients. The proposed statistic is based on the difference between full sample and rolling sample estimators of the sample covariance of the factors and the variable to be forecasted. Failure to reject the null ensures the structural stability of the factor augmented forecasting model. If the null is instead rejected, one can proceed to disentangle the cause of the rejection as being due to either (or both) of the afore mentioned varieties of instability. Standard inference can be carried out, as the suggested statistic has a chi-squared limiting distribution. We also establish the first order validity of (block) bootstrap critical values. Finally, we provide an empirical illustration by testing for the structural stability of factor augmented forecasting models for 11 U.S. macroeconomic indicators.

Suggested Citation

  • Valentina Corradi & Norman Swanson, 2013. "Testing for Structural Stability of Factor Augmented Forecasting Models," Departmental Working Papers 201314, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201314
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    References listed on IDEAS

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    1. repec:eme:aecozz:s0731-905320150000035011 is not listed on IDEAS
    2. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    3. Laurent Callot & Johannes Tang Kristensen, 2016. "Regularized Estimation of Structural Instability in Factor Models: The US Macroeconomy and the Great Moderation," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 437-479 Emerald Publishing Ltd.
    4. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    5. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2016. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1511-1543.
    6. Ruiz Ortega, Esther & Vicente Maldonado, Javier de, 2017. "Accurate Subsampling Intervals of Principal Components Factors," DES - Working Papers. Statistics and Econometrics. WS 23974, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Luke Hartigan, 2015. "Changes in the Factor Structure of the U.S. Economy: Permanent Breaks or Business Cycle Regimes?," Discussion Papers 2015-17, School of Economics, The University of New South Wales.
    8. Baltagi, Badi H. & Kao, Chihwa & Wang, Fa, 2017. "Identification and estimation of a large factor model with structural instability," Journal of Econometrics, Elsevier, vol. 197(1), pages 87-100.
    9. Erdenebat Bataa & Denise R.Osborn & Marianne Sensier, 2016. "China's Increasing Global Influence: Changes in International Growth Spillovers," Centre for Growth and Business Cycle Research Discussion Paper Series 221, Economics, The Univeristy of Manchester.
    10. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    11. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    12. Matteo Barigozzi & Lorenzo Trapani, 2017. "Sequential testing for structural stability in approximate factor models," Papers 1708.02786, arXiv.org, revised Mar 2018.
    13. 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..
    14. repec:eee:ecolet:v:161:y:2017:i:c:p:141-145 is not listed on IDEAS
    15. repec:eee:macchp:v2-415 is not listed on IDEAS
    16. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2017. "Identification of Global and National Shocks in International Financial Markets via General Dynamic Factor Models," Working Papers ECARES ECARES 2017-10, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    diffusion index; factor loading stability; forecast failure; forecast stability; regression coefficient stability;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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