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Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models

Matteo Barigozzi

arXiv 19 Jul 2023 · Econometrics · 1 citations (OpenAlex)

arXiv:2307.09864 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper investigates the properties of Quasi Maximum Likelihood estimation of an approximate factor model for an $n$-dimensional vector of stationary time series. We prove that the factor loadings estimated by Quasi Maximum Likelihood are asymptotically equivalent, as $n\to\infty$, to those estimated via Principal Components. Both estimators are, in turn, also asymptotically equivalent, as $n\to\infty$, to the unfeasible Ordinary Least Squares estimator we would have if the factors were observed. We also show that the usual sandwich form of the asymptotic covariance matrix of the Quasi Maximum Likelihood estimator is asymptotically equivalent to the simpler asymptotic covariance matrix of the unfeasible Ordinary Least Squares. All these results hold in the general case in which the idiosyncratic components are cross-sectionally heteroskedastic, as well as serially and cross-sectionally weakly correlated. The intuition behind these results is that as $n\to\infty$ the factors can be considered as observed, thus showing that factor models enjoy a blessing of dimensionality.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bai, J. and K. Li (2016) Maximum likelihood estimation and inference for approximate factor models of high dimension1.000329100%
2Bai, J (2003) Inferential theory for factor models of large dimensions1.000185100%
3Bai, J. and K. Li (2012) Statistical analysis of factor models of high dimension1.000159100%
4Lawley, D. N. and A. E. Maxwell (1971) Factor Analysis as a Statistical Method1.00055100%
5Merikoski, J. K. and R. Kumar (2004) Inequalities for spreads of matrix sums and products0.92843100%
6Tipping, M. E. and C. M. Bishop (1999) Probabilistic principal component analysis0.84333100%
7Doz, C., D. Giannone, and L. Reichlin (2012) A quasi maximum likelihood approach for large approximate dynamic factor models0.73732100%
8Anderson, T. W. and H. Rubin (1956) Statistical inference in factor analysis0.64422100%
9Bernanke, B. S., J. Boivin, and P. S. Eliasz (2005) Measuring the effects of monetary policy: A Factor-Augmented Vector Autoregressive (FAVAR) approach0.64422100%
10Breitung, J. and J. Tenhofen (2011) GLS estimation of dynamic factor models0.64422100%

Showing the top 10 of 42 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Quasi Maximum Likelihood Estimation and Inference .2cm of Large Approximate Dynamic Factor Models .2cm via the EM algorithm -.2cm1.000198
2Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review0.87452