Matteo Barigozzi, Matteo Luciani
arXiv 9 Oct 2019 · Mathematics — Statistics Theory · publishedFinance and Economics Discussion Series (2024) · 12 citations (OpenAlex)
arXiv:1910.03821 · PDF · DOI · OpenAlex · Extracted main text
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 the cross-sectional dimension, $n$, and the sample size, $T$, diverge to infinity: (i) the estimated loadings are $\sqrt T$-consistent, asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are $\sqrt n$-consistent, 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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bai, J. and K. Li (2016) Maximum likelihood estimation and inference for approximate factor models of high dimension | 1.000 | 27 | 8 | 100% |
| 2 | Bai, J (2003) Inferential theory for factor models of large dimensions | 1.000 | 21 | 7 | 100% |
| 3 | Barigozzi, M (2023) Asymptotic equivalence of principal component and quasi maximum likelihood estimators in large approximate factor models self | 1.000 | 19 | 8 | 100% |
| 4 | Merikoski, J. K. and R. Kumar (2004) Inequalities for spreads of matrix sums and products | 1.000 | 19 | 6 | 100% |
| 5 | Doz, C., D. Giannone, and L. Reichlin (2012) A quasi maximum likelihood approach for large approximate dynamic factor models | 1.000 | 14 | 7 | 100% |
| 6 | Bai, J. and K. Li (2012) Statistical analysis of factor models of high dimension | 1.000 | 9 | 5 | 100% |
| 7 | Hamilton, J. D (1994) Time Series Analysis | 1.000 | 6 | 4 | 100% |
| 8 | Fan, J., Y. Liao, and M. Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements | 1.000 | 6 | 3 | 100% |
| 9 | Wu, J. C. F (1983) On the convergence properties of the EM algorithm | 1.000 | 6 | 3 | 100% |
| 10 | Doz, C., D. Giannone, and L. Reichlin (2011) A two-step estimator for large approximate dynamic factor models based on Kalman filtering | 0.928 | 4 | 3 | 100% |
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