GLS Estimation of Dynamic Factor Models

• Published in: Journal of the American Statistical Association Vol. 106; no. 495; pp. 1150 - 1166
• Main Authors: Breitung, Jörg, Tenhofen, Jörn
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2011; American Statistical Association; Taylor & Francis Ltd
• Subjects: Analytical estimating; Applications; Autocorrelation; Consistent estimators; Correlations; Covariance; Covariance matrices; Datasets; Diffusion index; Distribution; Distribution theory; Error; Estimate reliability; Estimation; Estimators; Exact sciences and technology; Factor models; General topics; Generalized least squares; Heteroscedasticity; Limit theorems; Mathematics; Methodology; Monte Carlo simulation; Parameter estimation; Principal components; Probability and statistics; Probability theory and stochastic processes; Sampling; Sciences and techniques of general use; Serial correlation; Statistical discrepancies; Statistics; Theory and Methods; Generalized least squares; Statistical distribution; Error estimation; Sample size; Generalized least square; Generalized function; Serial correlation; Multivariate analysis; Stochastic method; Correspondence analysis; Estimator efficiency; Covariance; Limit distribution; Least squares method; Approximation theory; Factor models; Dynamic model; Sample survey; Principal components; Monte Carlo method; Factor analysis; Factor model; Statistical estimation; Heteroscedasticity; Statistical method; Numerical analysis; Sampling theory; Correlation analysis; Small sample property; Principal component analysis
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2011.tm09693

In this article a simple two-step estimation procedure of the dynamic factor model is proposed. The estimator allows for heteroscedastic and serially correlated errors. It turns out that the feasible two-step estimator has the same limiting distribution as the generalized least squares (GLS) estimator assuming that the covariance parameters are known. In a Monte Carlo study of the small sample properties, we find that the GLS estimators may be substantially more efficient than the usual estimator based on principal components. Furthermore, it turns out that the iterated version of the estimator may feature considerably improved properties in sample sizes usually encountered in practice.