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Information, data dimension and factor structure

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  • Jacobs, Jan P.A.M.
  • Otter, Pieter W.
  • den Reijer, Ard H.J.

Abstract

This paper employs concepts from information theory for choosing the dimension of a data set. We propose a relative information measure connected to Kullback–Leibler numbers. By ordering the series of the data set according to the measure, we are able to obtain a subset of a data set that is most informative. The method can be used as a first step in the construction of a dynamic factor model or a leading index, as illustrated with a Monte Carlo study and with the US macroeconomic data set of Stock and Watson [20].

Suggested Citation

  • Jacobs, Jan P.A.M. & Otter, Pieter W. & den Reijer, Ard H.J., 2012. "Information, data dimension and factor structure," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 80-91.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:80-91
    DOI: 10.1016/j.jmva.2011.11.003
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    1. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    2. Otter, Pieter W. & Jacobs, Jan P.A.M., 2006. "On information in static and dynamic factor models," CCSO Working Papers 200605, University of Groningen, CCSO Centre for Economic Research.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    5. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    6. Otter, Pieter W. & Jacobs, Jan P.A.M. & Reijer, Ard H.J. de, 2014. "A criterion for the number of factors in a data-rich environment," Research Report 14008-EEF, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    7. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    8. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    9. Robert Inklaar & Jan Jacobs & Ward Romp, 2005. "Business Cycle Indexes: Does a Heap of Data Help?," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2004(3), pages 309-336.
    10. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    11. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
    12. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    13. Jan Jacobs & Pieter Otter, 2008. "Determining the Number of Factors and Lag Order in Dynamic Factor Models: A Minimum Entropy Approach," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 385-397.
    14. Bai, Jushan & Ng, Serena, 2008. "Large Dimensional Factor Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(2), pages 89-163, June.
    15. 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.
    16. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    17. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
    18. 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. Klaus Abberger & Michael Graff & Boriss Siliverstovs & Jan-Egbert Sturm, 2014. "The KOF Economic Barometer, Version 2014," KOF Working papers 14-353, KOF Swiss Economic Institute, ETH Zurich.
    2. Ard Reijer, 2013. "Forecasting Dutch GDP and inflation using alternative factor model specifications based on large and small datasets," Empirical Economics, Springer, vol. 44(2), pages 435-453, April.

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    More about this item

    Keywords

    Kullback–Leibler numbers; Information; Factor structure; Data set dimension; Dynamic factor models; Leading index;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access

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