Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

Matteo Barigozzi and Matteo Luciani

No 2024-086, Finance and Economics Discussion Series from Board of Governors of the Federal Reserve System (U.S.)

Abstract: We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both n and T diverge to infinity: (i) the estimated loadings are \\sqrt{T}-consistent and asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are \\sqrt{n}-consistent and asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough.

Keywords: Approximate Dynamic Factor Model; Expectation Maximization Algorithm; Kalman Smoother; Quasi Maximum Likelihood (search for similar items in EconPapers)
JEL-codes: C32 C55 C58 (search for similar items in EconPapers)
Pages: 135 p.
Date: 2024-10-24
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Working Paper: Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:fip:fedgfe:2024-86

DOI: 10.17016/FEDS.2024.086

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