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EFFICIENT ESTIMATION OF FACTOR MODELS

Published online by Cambridge University Press:  02 August 2011

In Choi
In Choi*
Affiliation:
Sogang University
*
*Address correspondence to In Choi, Department of Economics, Sogang University, #1 Shinsu-dong, Mapo-gu, Seoul, Korea; e-mail: [email protected], [email protected].
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Abstract

This paper considers the factor model Xt = ΛFt + et. Assuming a normal distribution for the idiosyncratic error et conditional on the factors {Ft}, conditional maximum likelihood estimators of the factor and factor-loading spaces are derived. These estimators are called generalized principal component estimators (GPCEs) without the normality assumption. This paper derives asymptotic distributions of the GPCEs of the factor and factor-loading spaces. It is shown that variance of the GPCE of the common component is smaller than that of the principal component estimator studied in Bai (2003, Econometrica 71, 135–172). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component estimator. The feasible GPCE (FGPCE) of the factor space is shown to be asymptotically equivalent to the GPCE. The GPCE and FGPCE are shown to be more efficient than the principal component estimator in finite samples.

Type
ARTICLES
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 274 - 308
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Artis, M., Banerjee, A., & Marcellino, M. (2005) Factor forecasts for the U.K. Journal of Forecasting 24, 279–298.CrossRefGoogle Scholar
Bai, J. (2003) Inferential theory for factor models of large dimensions. Econometrica 71, 135–172.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2002) Determining the number of factors in approximate factor models. Econometrica 70, 191–221.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2004) A PANIC attack on unit roots and cointegration. Econometrica 72, 1127–1177.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2006) Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions. Econometrica 74, 1133–1150.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2010) Instrumental variable estimation in a data rich environment. Econometric Theory 26, 1577–1606.CrossRefGoogle Scholar
Basilevsky, A. (1994) Statistical Factor Analysis and Related Methods. Wiley.CrossRefGoogle Scholar
Bernanke, B., Boivin, J., & Eliasz, P. (2005) Measuring the effects of monetary policy: A factor-augmented vector autoregressive (FAVAR) approach. Quarterly Journal of Economics 120, 387–422.Google Scholar
Boivin, J. & Ng, S. (2006) Are more data always better for factor analysis? Journal of Econometrics 132, 169–194.CrossRefGoogle Scholar
Breitung, J. & Tenhofen, J. (2007) GLS Estimation of Dynamic Factor Models. Mimeo, University of Bonn.Google Scholar
Brillinger, D.R. (1981) Time Series. Data Analysis and Theory. Holden Day.Google Scholar
Chamberlain, G. & Rothschild, M. (1983) Arbitrage, factor structure, and mean variance analysis on large asset markets. Econometrica 51, 1281–1304.CrossRefGoogle Scholar
Connor, G. & Korajzcyk, R. (1986) Performance measurement with the arbitrage pricing theory: A new framework for analysis. Journal of Financial Economics 15, 373–394.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Cambridge University Press.CrossRefGoogle Scholar
Favero, C., Marcellino, M., & Neglia, F. (2005) Principal components at work: The empirical analysis of monetary policy with large data sets. Journal of Applied Econometrics 20, 603–620.CrossRefGoogle Scholar
Forni, M., Hallin, M., Lippi, M., & Reichlin, L. (2000) The generalized dynamic factor model: Identification and estimation. Review of Economics and Statistics 80, 540–554.CrossRefGoogle Scholar
Forni, M., Hallin, M., Lippi, M., & Reichlin, L. (2003) Do financial variables help in forecasting inflation and real activity in the euro area? Journal of Monetary Economics 50, 1243–1255.CrossRefGoogle Scholar
Forni, M., Hallin, M., Lippi, M., & Reichlin, L. (2005) The generalized dynamic factor model: One-sided estimation and forecasting. Journal of the American Statistical Association 100, 830–840.CrossRefGoogle Scholar
Huang, H., Lee, T.-H., & Li, C. (2006) Forecasting Output Growth and Inflation: How to Use Information in the Yield Curve. Mimeo, University of California, Riverside.Google Scholar
Jones, C.S. (2001) Extracting factors from heteroskedastic asset returns. Journal of Financial Economics 62, 293–325.CrossRefGoogle Scholar
Kapetanios, G. & Marcellino, M. (2006) A Parametric Estimation Method for Dynamic Factor Models of Large Dimensions. Mimeo, Queen Mary, University of London.CrossRefGoogle Scholar
Kruskal, W. (1968) When are Gauss-Markov and least squares estimators identical? A coordinate-free approach. Annals of Mathematical Statistics 39, 70–75.CrossRefGoogle Scholar
Ludvigson, S.C. & Ng, S. (2007) The empirical risk–return relation: A factor analysis approach. Journal of Financial Economics 83, 171–222.CrossRefGoogle Scholar
Magnus, J.R. & Neudecker, H. (1988) Matrix Differential Calculus. Wiley.Google Scholar
Moon, H.R. & Perron, B. (2004) Testing for a unit root in panels with dynamic factors. Journal of Econometrics 122, 81–126.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Phillips, P.C.B. & Sul, D. (2003) Dynamic panel estimation and homogeneity testing under cross section dependence. Econometrics Journal 6, 217–259.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (1999) Forecasting inflation. Journal of Monetary Economics 44, 293–335.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2002a) Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97, 1167–1179.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2002b) Macroeconomic forecasting using diffusion indexes. Journal of Business & Economic Statistics 20, 147–162.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2005) Implications of Dynamic Factor Model for VAR Analysis. NBER Working paper no. W11467.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2006) Forecasting with many predictors. In Elliott, G., Granger, C.W.J., & Timmerman, A. (eds.), Handbook of Economic Forecasting, pp. 515–554, Elsevier.CrossRefGoogle Scholar
Zyskind, G. (1967) On canonical forms, non-negative covariance matrices and best and simple least squares estimators in linear models. Annals of Mathematical Statistics 38, 1092–1109.CrossRefGoogle Scholar