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The Canonical Decomposition of Factor Models: Weak Factors are Everywhere

Philipp Gersing, Matteo Barigozzi, Christoph Rust, Manfred Deistler

arXiv 13 Jul 2023 · Econometrics · 1 citations (OpenAlex)

arXiv:2307.10067 · PDF · DOI · OpenAlex · Extracted main text

Abstract

There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with lags. In this paper we derive a canonical decomposition which nests both models by introducing the weak common component which is the difference between the dynamic- and the static common component. Such component is driven by potentially infinitely many non-pervasive weak factors which live in the dynamically common space (not to be confused with rate-weak factors, being pervasive but associated with a slower rate). Our result shows that the relation between the two approaches is far more rich and complex than what usually assumed. We exemplify why the weak common component shall not be neglected by means of theoretical and empirical examples. Furthermore, we propose a simple estimation procedure for the canonical decomposition. Our empirical estimates on US macroeconomic data reveal that the weak common component can account for a large part of the variation of individual variables. Furthermore in a pseudo real-time forecasting evaluation for industrial production and inflation, we show that gains can be obtained from considering the dynamic approach over the static approach.

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63
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Forni, M., Hallin, M., Lippi, M., and Reichlin, L (2000) The generalized dynamic-factor model: Identification and estimation1.000145100%
2Onatski, A (2012) Asymptotics of the principal components estimator of large factor models with weakly influential factors1.00075100%
3Forni, M., Giannone, D., Lippi, M., and Reichlin, L (2009) Opening the black box: Structural factor models with large cross sections1.00063100%
4Stock, J. H. and Watson, M. W (2002) Macroeconomic forecasting using diffusion indexes1.00063100%
5Forni, M., Hallin, M., Lippi, M., and Reichlin, L (2005) The generalized dynamic factor model: one-sided estimation and forecasting1.00054100%
6Bai, J. and Ng, S (2023) Approximate factor models with weaker loadings1.00053100%
7Forni, M., Hallin, M., Lippi, M., and Zaffaroni, P (2015) Dynamic factor models with infinite-dimensional factor spaces: One-sided representations1.00053100%
8Stock, J. H. and Watson, M. W (2002) Forecasting using principal components from a large number of predictors0.9619589%
9Bai, J (2003) Inferential theory for factor models of large dimensions0.9619489%
10Bai, J. and Ng, S (2002) Determining the number of factors in approximate factor models0.9285480%

Showing the top 10 of 63 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Principal Component Analysis .3cm for High-Dimensional Approximate Factor Models in Time Series: Assumptions, Asymptotic Theory, and Identification0.64422