arXiv 21 Aug 2024 · Econometrics
arXiv:2408.11676 · PDF · DOI · OpenAlex · Extracted main text
We show that in the approximate factor model the population normalised principal components converge in mean square (up to sign) under the standard assumptions for $n\to \infty$. Consequently, we have a generic interpretation of what the principal components estimator is actually identifying and existing results on factor identification are reinforced and refined. Based on this result, we provide a new asymptotic theory for the approximate factor model entirely without rotation matrices. We show that the factors space is consistently estimated with finite $T$ for $n\to \infty$ while consistency of the factors a.k.a the $L^2$ limit of the normalised principal components requires that both $(n, T)\to \infty$.
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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 | Barigozzi, M (2022) On estimation and inference of large approximate dynamic factor models via the principal component analysis | 1.000 | 6 | 3 | 100% |
| 2 | Wilkinson, J (1965) Algebraic Eigenvalue Problem | 1.000 | 5 | 3 | 100% |
| 3 | Bai, J. and Ng, S (2002) Determining the number of factors in approximate factor models | 0.874 | 5 | 2 | 100% |
| 4 | Bai, J (2003) Inferential theory for factor models of large dimensions | 0.811 | 4 | 2 | 100% |
| 5 | Bai, J. and Ng, S (2013) Principal components estimation and identification of static factors | 0.737 | 3 | 2 | 100% |
| 6 | Forni, M., Hallin, M., Lippi, M., and Reichlin, L (2004) The generalized dynamic factor model consistency and rates | 0.644 | 2 | 2 | 100% |
| 7 | Gersing, P (2023) Reconciling the Theory of Static and Dynamic Factor Sequences self | 0.644 | 2 | 2 | 100% |
| 8 | Stock, J. H. and Watson, M. W (2002) Forecasting using principal components from a large number of predictors | 0.511 | 2 | 1 | 100% |
| 9 | Bai, J. and Ng, S (2006) Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions | 0.405 | 1 | 1 | 100% |
| 10 | Bai, J. and Ng, S (2020) Simpler proofs for approximate factor models of large dimensions | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 19 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Principal Component Analysis .3cm for High-Dimensional Approximate Factor Models in Time Series: Assumptions, Asymptotic Theory, and Identification | 0.511 | 2 | 1 |