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Tests for Parameter Instability in Dynamic Factor Models

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  • Xu Han
  • Atsushi Inoue

Abstract

We develop tests for structural breaks of factor loadings in dynamic factor models. We focus on the joint null hypothesis that all factor loadings are constant over time. Because the number of factor loading parameters goes to infinity as the sample size grows, conventional tests cannot be used. Based on the fact that the presence of a structural change in factor loadings yields a structural change in second moments of factors obtained from the full sample principal component estimation, we reduce the infinite-dimensional problem into a finite-dimensional one and our statistic compares the pre- and post-break subsample second moments of estimated factors. Our test is consistent under the alternative hypothesis in which a fraction of or all factor loadings have structural changes. The Monte Carlo results show that our test has good finite-sample size and power.

Suggested Citation

  • Xu Han & Atsushi Inoue, 2011. "Tests for Parameter Instability in Dynamic Factor Models," TERG Discussion Papers 306, Graduate School of Economics and Management, Tohoku University, revised May 2013.
    • Handle: RePEc:toh:tergaa:306
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    File URL: http://hdl.handle.net/10097/56547
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    References listed on IDEAS

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    5. Chen, Liang & Dolado, Juan J. & Gonzalo, Jesús, 2014. "Detecting big structural breaks in large factor models," Journal of Econometrics, Elsevier, vol. 180(1), pages 30-48.
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    13. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
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    1. repec:eee:econom:v:198:y:2017:i:2:p:231-252 is not listed on IDEAS
    2. Pierre Perron & Tatsushi Oka, 2011. "Testing for Common Breaks in a Multiple Equations System," Boston University - Department of Economics - Working Papers Series WP2011-057, Boston University - Department of Economics.
    3. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    4. Chen, Liang & Dolado, Juan J. & Gonzalo, Jesús, 2014. "Detecting big structural breaks in large factor models," Journal of Econometrics, Elsevier, vol. 180(1), pages 30-48.
    5. Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.
    6. 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.
    7. Chen, Liang, 2015. "Estimating the common break date in large factor models," Economics Letters, Elsevier, vol. 131(C), pages 70-74.
    8. Chen, Liang, 2012. "Identifying observed factors in approximate factor models: estimation and hypothesis testing," MPRA Paper 37514, University Library of Munich, Germany.
    9. Jushan Bai & Kunpeng Li, 2016. "Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension," The Review of Economics and Statistics, MIT Press, vol. 98(2), pages 298-309, May.
    10. 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.
    11. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    12. repec:eee:eneeco:v:65:y:2017:i:c:p:411-423 is not listed on IDEAS
    13. Matteo Barigozzi & Lorenzo Trapani, 2017. "Sequential testing for structural stability in approximate factor models," Papers 1708.02786, arXiv.org, revised Mar 2018.
    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. 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.
    17. Antoine A. Djogbenou, 2017. "Comovements in the Real Activity of Developed and Emerging Economies: A Test of Global versus Specific International Factors," Working Papers 1392, Queen's University, Department of Economics.
    18. Dante Amengual & Luca Repetto, 2014. "Testing a Large Number of Hypotheses in Approximate Factor Models," Working Papers wp2014_1410, CEMFI.

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