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

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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.

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  • Matteo Barigozzi & Matteo Luciani, 2024. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Finance and Economics Discussion Series 2024-086, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2024-86
    DOI: 10.17016/FEDS.2024.086
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    Keywords

    Approximate Dynamic Factor Model; Expectation Maximization Algorithm; Kalman Smoother; Quasi Maximum Likelihood;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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