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Testing for Structural Stability of Factor Augmented Forecasting Models

  • Valentina Corradi

    ()

    (Warwick University)

  • Norman Swanson

    ()

    (Rutgers University)

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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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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  1. Rossi, Barbara & Giacomini, Raffaella, 2006. "Detecting and Predicting Forecast Breakdowns," Working Papers 06-01, Duke University, Department of Economics.
  2. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
  3. West, K.D. & McCracken, M.W., 1997. "Regression-Based Tests of Predictive Ability," Working papers 9710, Wisconsin Madison - Social Systems.
  4. Nii Ayi Armah & Norman Swanson, 2010. "Seeing Inside the Black Box: Using Diffusion Index Methodology to Construct Factor Proxies in Large Scale Macroeconomic Time Series Environments," Econometric Reviews, Taylor & Francis Journals, vol. 29(5-6), pages 476-510.
  5. Anindya Banerjee & Massimiliano Marcellino & Igor Masten, 2008. "Forecasting Macroeconomic Variables Using Diffusion Indexes in Short Samples with Structural Change," Working Papers 334, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. Goncalves, Silvia & White, Halbert, 2002. "Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models," University of California at San Diego, Economics Working Paper Series qt8hx21540, Department of Economics, UC San Diego.
  7. Peter Reinhard Hansen & Allan Timmermann, 2012. "Choice of Sample Split in Out-of-Sample Forecast Evaluation," CREATES Research Papers 2012-43, Department of Economics and Business Economics, Aarhus University.
  8. 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.
  9. Jennifer Castle & David Hendry, 2012. "Forecasting by factors, by variables, or both?," Economics Series Working Papers 600, University of Oxford, Department of Economics.
  10. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics.
  11. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
  12. 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.
  13. Jörg Breitung & Sandra Eickmeier, 2006. "Dynamic factor models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 27-42, March.
  14. Kim, Hyun Hak & Swanson, Norman R., 2014. "Forecasting financial and macroeconomic variables using data reduction methods: New empirical evidence," Journal of Econometrics, Elsevier, vol. 178(P2), pages 352-367.
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  16. Barbara Rossi & Atsushi Inoue, 2012. "Out-of-Sample Forecast Tests Robust to the Choice of Window Size," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 432-453, April.
  17. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
  18. 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.
  19. repec:oxf:wpaper:2002-w12 is not listed on IDEAS
  20. Michael P. Clements & David F. Hendry, 2002. "Modelling methodology and forecast failure," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 319-344, 06.
  21. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  22. Hyun Hak Kim & Norman Swanson, 2013. "Mining Big Data Using Parsimonious Factor and Shrinkage Methods," Departmental Working Papers 201316, Rutgers University, Department of Economics.
  23. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  24. Clements, Michael P. & Hendry, David F., 2006. "Forecasting with Breaks," Handbook of Economic Forecasting, Elsevier.
  25. Castle, Jennifer L. & Clements, Michael P. & Hendry, David F., 2013. "Forecasting by factors, by variables, by both or neither?," Journal of Econometrics, Elsevier, vol. 177(2), pages 305-319.
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