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Testing for Structural Stability of Factor Augmented Forecasting Models

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 201314.

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Length: 20 pages
Date of creation: 16 Jul 2013
Date of revision:
Handle: RePEc:rut:rutres:201314

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Related research

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

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References

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  1. Castle, Jennifer L. & Doornik, Jurgen A. & Hendry, David F., 2012. "Model selection when there are multiple breaks," Journal of Econometrics, Elsevier, vol. 169(2), pages 239-246.
  2. Michael P. Clements & David F. Hendry, 2002. "Modelling methodology and forecast failure," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 319-344, 06.
  3. repec:att:wimass:9710 is not listed on IDEAS
  4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  5. Chen, Liang & Dolado, Juan Jose & Gonzalo, Jesus, 2011. "Detecting big structural breaks in large factor models," MPRA Paper 31344, University Library of Munich, Germany.
  6. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
  7. Jennifer Castle & David Hendry, 2012. "Forecasting by factors, by variables, or both?," Economics Series Working Papers 600, University of Oxford, Department of Economics.
  8. Nii Ayi Armah & Norman R. Swanson, 2008. "Seeing inside the black box: Using diffusion index methodology to construct factor proxies in large scale macroeconomic time series environments," Working Papers 08-25, Federal Reserve Bank of Philadelphia.
  9. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  10. Raffella Giacomini & Barbara Rossi, 2005. "Detecting and Predicting Forecast Breakdowns," UCLA Economics Working Papers 845, UCLA Department of Economics.
  11. Breitung, Jörg & Eickmeier, Sandra, 2009. "Testing for structural breaks in dynamic factor models," Discussion Paper Series 1: Economic Studies 2009,05, Deutsche Bundesbank, Research Centre.
  12. Breitung, Jörg & Eickmeier, Sandra, 2005. "Dynamic factor models," Discussion Paper Series 1: Economic Studies 2005,38, Deutsche Bundesbank, Research Centre.
  13. Kenneth D. West & Michael W. McCracken, 1998. "Regression-Based Tests of Predictive Ability," NBER Technical Working Papers 0226, National Bureau of Economic Research, Inc.
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Cited by:
  1. Cheng, Xu & Liao, Zhipeng & Schorfheide, Frank, 2013. "Shrinkage estimation of high-dimensional factor models with structural instabilities," Working Papers 14-4, Federal Reserve Bank of Philadelphia.
  2. Xu Cheng & Zhipeng Liao & Frank Schorfheide, 2014. "Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities," NBER Working Papers 19792, National Bureau of Economic Research, Inc.

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