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Testing for time-varying loadings in dynamic factor models

Author

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  • Jeroen V.K. Rombouts
  • Jakob Guldbæk Mikkelsen

    (Aarhus University and CREATES)

Abstract

In this paper we develop a test for time-varying factor loadings in factor models. The test is simple to compute and is constructed from estimated factors and residuals using the principal components estimator. The hypothesis is tested by regressing the squared residuals on the squared factors. The squared correlation coefficient times the sample size has a limiting chi-squared distribution. The test can be made robust to serial correlation in the idiosyncratic errors. We find evidence for factor loadings variance in over half of the variables in a dataset for the US economy, while there is evidence of time-varying loadings on the risk factors underlying portfolio returns for around 80% of the portfolios.

Suggested Citation

  • Jeroen V.K. Rombouts & Jakob Guldbæk Mikkelsen, 2017. "Testing for time-varying loadings in dynamic factor models," CREATES Research Papers 2017-22, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2017-22
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    References listed on IDEAS

    as
    1. Breitung, Jörg & Tenhofen, Jörn, 2011. "GLS Estimation of Dynamic Factor Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1150-1166.
    2. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    3. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    4. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    5. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    6. Giannone, Domenico & Reichlin, Lucrezia & Sala, Luca, 2006. "VARs, common factors and the empirical validation of equilibrium business cycle models," Journal of Econometrics, Elsevier, vol. 132(1), pages 257-279, May.
    7. 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.
    8. 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.
    9. 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. Riccardo Borghi & Eric Hillebrand & Jakob Mikkelsen & Giovanni Urga, 2018. "The dynamics of factor loadings in the cross-section of returns," CREATES Research Papers 2018-38, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Factor models; principal components; LM test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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