arXiv 21 Mar 2023 · Econometrics · 2 citations (OpenAlex)
arXiv:2303.11777 · PDF · DOI · OpenAlex · Extracted main text
We review Quasi Maximum Likelihood estimation of factor models for high-dimensional panels of time series. We consider two cases: (1) estimation when no dynamic model for the factors is specified (Bai and Li, 2012, 2016); (2) estimation based on the Kalman smoother and the Expectation Maximization algorithm thus allowing to model explicitly the factor dynamics (Doz et al., 2012, Barigozzi and Luciani, 2019). Our interest is in approximate factor models, i.e., when we allow for the idiosyncratic components to be mildly cross-sectionally, as well as serially, correlated. Although such setting apparently makes estimation harder, we show, in fact, that factor models do not suffer of the {\it curse of dimensionality} problem, but instead they enjoy a {\it blessing of dimensionality} property. In particular, given an approximate factor structure, if the cross-sectional dimension of the data, $N$, grows to infinity, we show that: (i) identification of the model is still possible, (ii) the mis-specification error due to the use of an exact factor model log-likelihood vanishes. Moreover, if we let also the sample size, $T$, grow to infinity, we can also consistently estimate all parameters of the model and make inference. The same is true for estimation of the latent factors which can be carried out by weighted least-squares, linear projection, or Kalman filtering/smoothing. We also compare the approaches presented with: Principal Component analysis and the classical, fixed $N$, exact Maximum Likelihood approach. We conclude with a discussion on efficiency of the considered estimators.
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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 | 29 | 9 | 100% |
| 2 | Bai, J. and K. Li (2012) Statistical analysis of factor models of high dimension | 1.000 | 22 | 6 | 100% |
| 3 | Doz, C., D. Giannone, and L. Reichlin (2012) A quasi maximum likelihood approach for large approximate dynamic factor models | 1.000 | 13 | 8 | 100% |
| 4 | Barigozzi, M (2022) On estimation and inference of large approximate dynamic factor models via the principal component analysis self | 1.000 | 12 | 4 | 100% |
| 5 | Barigozzi, M. and M. Luciani (2019) Quasi maximum likelihood estimation and inference of large approximate dynamic factor models via the EM algorithm self | 1.000 | 11 | 4 | 100% |
| 6 | Bai, J (2003) Inferential theory for factor models of large dimensions | 1.000 | 10 | 5 | 100% |
| 7 | Lawley, D. N. and A. E. Maxwell (1971) Factor Analysis as a Statistical Method | 1.000 | 6 | 4 | 100% |
| 8 | Anderson, T. W. and H. Rubin (1956) Statistical inference in factor analysis | 1.000 | 5 | 3 | 100% |
| 9 | Breitung, J. and J. Tenhofen (2011) GLS estimation of dynamic factor models | 1.000 | 5 | 3 | 100% |
| 10 | Quah, D. and T. J. Sargent (1993) A dynamic index model for large cross sections | 1.000 | 5 | 3 | 100% |
Showing the top 10 of 161 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Modewise Additive Factor Model for Matrix Time Series | 0.405 | 1 | 1 |
| 2 | Learning Nonlinear Factor Models with Unknown Monotone Links from Incomplete and Noisy Data | 0.405 | 1 | 1 |