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Estimation of Approximate Factor Models: Is it Important to have a Large Number of Variables?

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Author Info
Chris Heaton () (Department of Economics, Macquarie University)
Victor Solo (University of New South Wales)

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Abstract

The use of principal component techniques to estimate approximate factor models with large cross-sectional dimension is now well established. However, recent work by Inklaar, Jacobs and Romp (2003) and Boivin and Ng (2005) has cast some doubt on the importance of a large cross-sectional dimension for the precision of the estimates. This paper presents some new theory for approximate factor model estimation. Consistency is proved and rates of convergence are derived under conditions that allow for a greater degree of cross-correlation in the model disturbances than previously published results. The rates of convergence depend on the rate at which the cross-sectional correlation of the model disturbances grows as the cross-sectional dimension grows. The consequences for applied economic analysis are discussed.

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File URL: http://www.econ.mq.edu.au/research/2006/HeatonEstimtnOfApproxFactorModels.pdf
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Publisher Info
Paper provided by Macquarie University, Department of Economics in its series Research Papers with number 0605.

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Length: 31 pages.
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:mac:wpaper:0605

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Postal: Sydney NSW 2109
Web page: http://www.econ.mq.edu.au/
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Related research
Keywords: Factor analysis; time series models; principal components;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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  1. Bernanke, Ben S. & Boivin, Jean, 2003. "Monetary policy in a data-rich environment," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 525-546, April. [Downloadable!] (restricted)
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  2. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!]
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  4. 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. [Downloadable!] (restricted)
  5. Christian Gillitzer & Jonathan Kearns & Anthony Richards, 2005. "The Australian Business Cycle: A Coincident Indicator Approach," RBA Annual Conference Volume, in: Christopher Kent & David Norman (ed.), The Changing Nature of the Business Cycle Reserve Bank of Australia. [Downloadable!]
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  6. 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. [Downloadable!] (restricted)
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  7. Altissimo, Filippo & Bassanetti, Antonio & Cristadoro, Riccardo & Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia & Veronese, Giovanni, 2001. "EuroCOIN: A Real Time Coincident Indicator of the Euro Area Business Cycle," CEPR Discussion Papers 3108, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  8. Schneeweiss, H. & Mathes, H., 1995. "Factor Analysis and Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 105-124, October. [Downloadable!] (restricted)
  9. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January. [Downloadable!] (restricted)
  10. K. Jöreskog, 1967. "Some contributions to maximum likelihood factor analysis," Psychometrika, Springer, vol. 32(4), pages 443-482, December. [Downloadable!] (restricted)
  11. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March. [Downloadable!] (restricted)
  12. Inklaar, Robert & Jacobs, Jan & Romp, Ward, 2003. "Business cycle indexes: does a heap of data help?," CCSO Working Papers 200312, University of Groningen, CCSO Centre for Economic Research. [Downloadable!]
  13. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January. [Downloadable!] (restricted)
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