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Information, data dimension and factor structure

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  • Jan Jacobs
  • Pieter Otter
  • Ard den Reijer

Abstract

This paper employs concepts from information theory to choosing the dimension of a data set. We calculate relative measures of information in the data in terms of eigenvalues and derive criteria to determine the `optimal' size of the data set, in particular whether an extra variable adds information. The methods can be used as a first step in the construction of a dynamic factor model or a leading index, as illustrated with a macroeconomic data set on The Netherlands.

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File URL: http://www.dnb.nl/binaries/Working%20Paper%20150_tcm46-164639.pdf
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Bibliographic Info

Paper provided by Netherlands Central Bank, Research Department in its series DNB Working Papers with number 150.

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Date of creation: Oct 2007
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Handle: RePEc:dnb:dnbwpp:150

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Keywords: information; data set dimension; dynamic factor models; leading index.;

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References

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  1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
  2. Robert Inklaar & Jan Jacobs & Ward Romp, 2004. "Business Cycle Indexes: Does a Heap of Data Help?," Journal of Business Cycle Measurement and Analysis, OECD Publishing,CIRET, vol. 2004(3), pages 309-336.
  3. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(06), pages 1113-1141, December.
  4. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
  5. 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.
  6. 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.
  7. 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.
  8. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, 09.
  9. 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.
  10. 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.
  11. 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.
  12. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  13. 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.
  14. 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.
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Cited by:
  1. 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.
  2. Klaus Abberger & Boriss Siliverstovs & Jan-Egbert Sturm & Michael Graff, 2014. "The KOF Economic Barometer, Version 2014: A Composite Leading Indicator for the Swiss Business Cycle," KOF Working papers 14-353, KOF Swiss Economic Institute, ETH Zurich.

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