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Asymptotic Principal Components Estimation Of Large Factor Models

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Author Info
Chris Heaton () (Department of Economics, Macquarie University)
Victor Solo (School of Electrical Engineering and Telecommunications, University of New South Wales)

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Abstract

There has been much recent interest in forecasting based on factor analysis models for large numbers of observable variables (p) and large numbers of observations (T). Some nice asymptotic results have been produced showing that under certain conditions, as (p,T) ? (8, 8) principal components analysis can be used to carry out the forecasting, thereby avoiding the need to fit a full factor analysis model. However, the question of how large p needs to be in order for the asymptotic theory to provide an adequate approximation in practice is open. In this paper we develop probability bounds for the forecast accuracy of principal component forecasts for stationary processes in terms of an empirically determinable noise to signal ratio. We develop a hypothesis test for this bound for which asymptotics in T hold even with p large and apply this test to US macrodata.

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Publisher Info
Paper provided by Macquarie University, Department of Economics in its series Research Papers with number 0303.

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Length: 21 pages.
Date of creation: Jun 2003
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Handle: RePEc:mac:wpaper:0303

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Web page: http://www.econ.mq.edu.au/
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  1. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September. [Downloadable!] (restricted)
  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)
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  3. Dhrymes, Phoebus J & Friend, Irwin & Gultekin, N Bulent, 1984. " A Critical Reexamination of the Empirical Evidence on the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 39(2), pages 323-46, June. [Downloadable!] (restricted)
  4. Breusch, Trevor S, 1986. "Hypothesis Testing in Unidentified Models," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 635-51, August. [Downloadable!] (restricted)
  5. 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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  6. Schneeweiss, H. & Mathes, H., 1995. "Factor Analysis and Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 105-124, October. [Downloadable!] (restricted)
  7. K. Jöreskog, 1967. "Some contributions to maximum likelihood factor analysis," Psychometrika, Springer, vol. 32(4), pages 443-482, December. [Downloadable!] (restricted)
  8. George Kapetanios, 2002. "Factor Analysis Using Subspace Factor Models: Some Theoretical Results and an Application to UK Inflation Forecasting," Working Papers 466, Queen Mary, University of London, Department of Economics. [Downloadable!]
  9. Chris Heaton & Victor Solo, 2002. "Identification and Estimation of Causal Factor Models of Stationary Time Series," Research Papers 0201, Macquarie University, Department of Economics. [Downloadable!]
  10. 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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