EFFICIENT ESTIMATION OF FACTOR MODELS

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.

[1]  George Kapetanios,et al.  A parametric estimation method for dynamic factor models of large dimensions , 2006 .

[2]  J. Stock,et al.  Forecasting Using Principal Components From a Large Number of Predictors , 2002 .

[3]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[4]  Christopher S. Jones,et al.  Extracting factors from heteroskedastic asset returns , 2001 .

[5]  Serena Ng,et al.  Are more data always better for factor analysis , 2006 .

[6]  Marco Lippi,et al.  The Generalized Dynamic Factor Model , 2002 .

[7]  Rob J Hyndman,et al.  25 years of time series forecasting , 2006 .

[8]  R. T. Lee,et al.  Forecasting Output Growth and In fl ation : How to Use Information in the Yield Curve ∗ , 2006 .

[9]  Alexander Basilevsky,et al.  Statistical Factor Analysis and Related Methods , 1994 .

[10]  Massimiliano Marcellino,et al.  Factor Forecasts for the UK , 2005 .

[11]  Mark W. Watson,et al.  Chapter 10 Forecasting with Many Predictors , 2006 .

[12]  J. Stock,et al.  Macroeconomic Forecasting Using Diffusion Indexes , 2002 .

[13]  J. Bai,et al.  Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions , 2006 .

[14]  Hyungsik Roger Moon,et al.  Testing For A Unit Root In Panels With Dynamic Factors , 2002 .

[15]  Victor Solo,et al.  Asymptotics for Linear Processes , 1992 .

[16]  Serena Ng,et al.  INSTRUMENTAL VARIABLE ESTIMATION IN A DATA RICH ENVIRONMENT , 2010, Econometric Theory.

[17]  Donggyu Sul,et al.  Dynamic Panel Estimation and Homogeneity Testing Under Cross Section Dependence , 2002 .

[18]  J. Breitung,et al.  GLS Estimation of Dynamic Factor Models , 2011 .

[19]  Jean Boivin,et al.  Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach , 2003 .

[20]  J. Davidson.  Stochastic Limit Theory , 1994 .

[21]  Michel Dubois-Violette.  $d^N=0$ , 1997 .

[22]  Sydney C. Ludvigson,et al.  The Empirical Risk-Return Relation: A Factor Analysis Approach , 2005 .

[23]  Jonathan H. Wright,et al.  Forecasting Inflation , 2011 .

[24]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[25]  J. Stock,et al.  Forecasting with Many Predictors , 2006 .

[26]  Marc Hallin,et al.  The Generalized Dynamic Factor Model. One-Sided Estimation and Forecasting , 2003 .

[27]  William Kruskal,et al.  When are Gauss-Markov and Least Squares Estimators Identical? A Coordinate-Free Approach , 1968 .

[28]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1982 .

[29]  M. Hallin,et al.  The Generalized Dynamic-Factor Model: Identification and Estimation , 2000, Review of Economics and Statistics.

[30]  Gregory Connor,et al.  Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis , 1985 .

[31]  J. Bai,et al.  Inferential Theory for Factor Models of Large Dimensions , 2003 .

[32]  Maurice Kendall,et al.  Time Series , 2009, Encyclopedia of Biometrics.

[33]  Helmut Lütkepohl,et al.  Introduction to multiple time series analysis , 1991 .

[34]  Marco Lippi,et al.  Do Financial Variables Help Forecasting Inflation and Real Activity in the Euro Area , 2002 .

[35]  J. Bai,et al.  A Panic Attack on Unit Roots and Cointegration , 2001 .

[36]  Massimiliano Marcellino,et al.  Principal components at work: the empirical analysis of monetary policy with large data sets , 2005 .

[37]  C. Granger,et al.  Handbook of Economic Forecasting , 2006 .

[38]  George Zyskind,et al.  On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models , 1967 .