arXiv 19 Jul 2023 · Econometrics · 1 citations (OpenAlex)
arXiv:2307.09864 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
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 | 32 | 9 | 100% |
| 2 | Bai, J (2003) Inferential theory for factor models of large dimensions | 1.000 | 18 | 5 | 100% |
| 3 | Bai, J. and K. Li (2012) Statistical analysis of factor models of high dimension | 1.000 | 15 | 9 | 100% |
| 4 | Lawley, D. N. and A. E. Maxwell (1971) Factor Analysis as a Statistical Method | 1.000 | 5 | 5 | 100% |
| 5 | Merikoski, J. K. and R. Kumar (2004) Inequalities for spreads of matrix sums and products | 0.928 | 4 | 3 | 100% |
| 6 | Tipping, M. E. and C. M. Bishop (1999) Probabilistic principal component analysis | 0.843 | 3 | 3 | 100% |
| 7 | Doz, C., D. Giannone, and L. Reichlin (2012) A quasi maximum likelihood approach for large approximate dynamic factor models | 0.737 | 3 | 2 | 100% |
| 8 | Anderson, T. W. and H. Rubin (1956) Statistical inference in factor analysis | 0.644 | 2 | 2 | 100% |
| 9 | Bernanke, B. S., J. Boivin, and P. S. Eliasz (2005) Measuring the effects of monetary policy: A Factor-Augmented Vector Autoregressive (FAVAR) approach | 0.644 | 2 | 2 | 100% |
| 10 | Breitung, J. and J. Tenhofen (2011) GLS estimation of dynamic factor models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 42 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.