Bai, Jushan and Li, Kunpeng (2012): Maximum likelihood estimation and inference for approximate factor models of high dimension.
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Abstract
An approximate factor model of high dimension has two key features. First, the idiosyncratic errors are correlated and heteroskedastic over both the crosssection and time dimensions; the correlations and heteroskedasticities are of unknown forms. Second, the number of variables is comparable or even greater than the sample size. Thus a large number of parameters exist under a high dimensional approximate factor model. Most widely used approaches to estimation are principal component based. This paper considers the maximum likelihoodbased estimation of the model. Consistency, rate of convergence, and limiting distributions are obtained under various identification restrictions. Comparison with the principal component method is made. The likelihoodbased estimators are more efficient than those of principal component based. Monte Carlo simulations show the method is easy to implement and an application to the U.S. yield curves is considered
Item Type:  MPRA Paper 

Original Title:  Maximum likelihood estimation and inference for approximate factor models of high dimension 
Language:  English 
Keywords:  Factor analysis; Approximate factor models; Maximum likelihood; Kalman smoother, Principal components; Inferential theory 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C33  Models with Panel Data; Longitudinal Data; Spatial Time Series 
Item ID:  42118 
Depositing User:  Jushan Bai 
Date Deposited:  25. Oct 2012 10:42 
Last Modified:  14. Feb 2013 09:30 
References:  Amemiya Y., W. A. Fuller and S. G. Pantula (1987) The asymptotic distributions of some estimators for a factor analysis model, \textit{Journal of Multivariate Analysis}, \textbf{22:1}, 5164. Anderson, T. W. (2003) \textit{An Introduction to Multivariate Statistical Analysis}, John Wily \& Sons. Anderson, T. W. and Y. Amemiya (1988) The asymptotic normal distribution of estimators in factor analysis under general conditions, \textit{The Annals of Statistics}, \textbf{16:2}, 759771. Anderson, T. W. and H. Rubin (1956) Statistical inference in factor analysis, In \textit{ Proceedings of the third Berkeley Symposium on mathematical statistics and probability: contributions to the theory of statistics}, University of California Press. Bai, J. (2003) Inferential theory for factor models of large dimensions. \textit{Econometrica}, \textbf{71(1)}, 135171. Bai, J. and K. Li (2012) Statistical analysis of factor models of high dimension, \textit{The Annals of Statistics}, \textbf{40:1}, 436465. Bai, J. and S. Ng (2002) Determining the number of factors in approximate factor models,\textit{ Econometrica}, \textbf{70:1}, 191221. Bernanke, B. S. and J. Boivin (2003) Monetary policy in a datarich environment, \textit{Journal of Monetary Economics}, \textbf{50:3}, 525546 Bernanke, B. S., J. Boivin, and P. Eliasz (2005) Measuring the effects of monetary policy: a factoraugmented vector autoregressive (FAVAR) approach, \textit{The Quarterly Journal of Economics}, \textbf{120:1} 387422 Breitung, J. and J. Tenhofen (2011) GLS estimation of dynamic factor models, \textit{ Journal of the American Statistical Association}, 106, 11501156. Chamberlain, G. and M. Rothschild (1983) Arbitrage, factor structure, and meanvariance analysis on large asset markets, \textit{Econometrica}, \textbf{51:5}, 12811304. Choi, I. (2007) Efficient Estimation of Factor Models, \textit{Econometric theory}, forthcoming. Connor, G. and R. A. Korajczyk (1988) Risk and return in an equilibrium APT: Application of a new test methodology, \textit{Journal of Financial Economics}, \textbf{21:2}, 255289. Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm. {\em Journal of the Royal Statistical Society,} Series B, 39, 138. Diebold, F and C. Li (2006) Forecasting the term structure of government bond yields, \textit{Journal of Econometrics}, \textbf{130:2}, 337364. Diebold, F.X., G.D. Rudebusch and B. S. Aruoba (2006) The macroeconomy and the yield curve: a dynamic latent factor approach, \textit{Journal of Econometrics}, \textbf{131:1}, 309338. Doz, C., D. Giannone, and L. Reichlin (2011a), A qausimaximum likelihood approach for large approximate dynamic factor models, \textit{Review of economics and statistics}, forthcoming. Doz, C., D. Giannone, and L. Reichlin (2011b), A TwoStep estimator for large approximate dynamic factor models based on Kalman filtering, \textit{Journal of Econometrics}, \text{164:1}, 188205. Fan, J., Y. Liao, and M. Mincheva (2011). High Dimensional Covariance Matrix Estimation in Approximate Factor Models. {\em Annals of Statistics}, 39, 33203356. Forni, M., M. Hallin, M. Lippi and L. Reichlin (2000), The generalized dynamicfactor model: Identification and estimation. \textit{ Review of Economics and Statistics}, \text{82(4)}: 540554. Goyal, A. C. Perignon, C. Villa (2008), How common are common return factors across the NYSE and Nasdaq, {\em Journal of Financial Economics,} 252271. Inoue, A. and X. Han (2011) Tests for Parameter Instability in Dynamic Factor Models. Department of Economics, North Carolina State University. Jenrich, R. I. (1969) Asymptotic properties of nonlinear least squares estimators, \textit{The Annals of Mathematical Statistics}, \textbf{40(2)}:633643. Jungbacker, B. and S.J. Koopman (2008), Likelihoodbased analysis for dynamic factor models, unpublished manuscript, Tinbergen Institute. Kose, M. A. and C. Otrok, and C.H. Whiteman (2003), International business cycles: World, region, and countryspecific factors, \textit{American Economic Review}, \textbf{93(4)}: 12161239. Lawley D. N. and A. E. Maxwell (1971), \textit{Factor Analysis as a Statistical Method}, New York: American Elsevier Publishing Company. Meng, X.L. and D.B. Rubin (1993), Maximum likelihood estimation via the ECM algorithm: a genenral framework, \textit{Biometrika}, \textbf{80(2)}, 267278. Nelson, C.R. and A.F. Siegel (1987) Parsimonious modeling of yield curves, \textit{Journal of Business}, \textbf{60(4)}, 473489. Newey, W.K. and D. McFadden (1994) Large sample estimation and hypothesis testing, \textit{Handbook of econometrics}, Vol.4, 21112245 Quah, D. and T. Sargent (1992). A dynamic index model for large crosssection. Federal Reserve Bank of Minneapolis, Discussion Paper 77. In James Stock and Mark Watson, editors, Business Cycle, pages 161200. Univeristy of Chicago Press, 1992. Ross, S. A. (1976) The arbitrage theory of capital asset pricing, \textit{Journal of Economic Theory},\textbf{13:3}, 341360. Stock, J. H. and M. W. Watson (2002a) Macroeconomic forecasting using diffusion indexes" {\em Journal of Business and Economic Statistics}, 20, 147162. Stock, J. H. and M. W. Watson (2002b) Forecasting using principal components from a large number of predictors, {\em Journal of the American Statistical Association,} \textbf{97}, 11671179. Wang, P. (2010) Large dimensional factor models with a multilevel factor structure: identification, estimation, and inference. Department of Economics, HKUST. Watson, M.W. and R.F. Engle. (1983) Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models. {\em Journal of Econometrics}, 23(3):385400, 1983. Wu, C.F.J. (1981) Asymptotic theory of nonlinear least squares estimation, \textit{The Annals of Statistics}, 501513. Wu, C.F.J. (1983) On the convergence properties of the EM algorithm, {\em The Annals of Statistics}, 95103. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/42118 
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Maximum likelihood estimation and inference for approximate factor models of high dimension. (deposited 21. Oct 2012 17:58)
 Maximum likelihood estimation and inference for approximate factor models of high dimension. (deposited 25. Oct 2012 10:42) [Currently Displayed]