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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].

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 106 (2012)
Issue (Month): C ()
Pages: 80-91

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Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:80-91

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Related research

Keywords: Kullback–Leibler numbers; Information; Factor structure; Data set dimension; Dynamic factor models; Leading index;

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References

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  1. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2509, C.E.P.R. Discussion Papers.
  2. 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.
  3. Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000. "The generalised dynamic factor model: identification and estimation," ULB Institutional Repository 2013/10143, ULB -- Universite Libre de Bruxelles.
  4. 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.
  5. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, Econometric Society, vol. 77(5), pages 1447-1479, 09.
  6. 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, American Statistical Association, vol. 97, pages 1167-1179, December.
  7. 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, American Statistical Association, vol. 102, pages 603-617, June.
  8. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 25, pages 52-60, January.
  9. Jean Boivin & Serena Ng, 2003. "Are More Data Always Better for Factor Analysis?," NBER Working Papers 9829, National Bureau of Economic Research, Inc.
  10. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  11. Otter, Pieter W. & Jacobs, Jan P.A.M., 2006. "On information in static and dynamic factor models," CCSO Working Papers, University of Groningen, CCSO Centre for Economic Research 200605, University of Groningen, CCSO Centre for Economic Research.
  12. 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, Taylor & Francis Journals, vol. 27(4-6), pages 385-397.
  13. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 135-171, January.
  14. 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.
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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, 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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