Journal of Econometrics· 2026Q1
The canonical decomposition of factor models: weak factors are everywhere
- 8citations
- Q1SCImago
- 2026year
Short summary
A novel canonical decomposition of factor models reveals a 'weak common component' driven by non-pervasive weak factors, which should not be neglected and can yield more plausible impulse response functions.
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Key points
- Introduces a novel canonical decomposition for factor models, integrating static and dynamic factor models.
- Identifies a 'weak common component' driven by non-pervasive weak factors within the dynamically common space.
- Demonstrates the significance of the weak common component in U.S. macroeconomic indicators and global financial volatilities.
- Shows that accounting for weak common components results in more plausible Impulse Response Functions.
- Provides consistent estimators for all components of the decomposition and for the weak factors.
AI-generated from the title and abstract; the full text is not read.
Abstract
We derive a novel canonical decomposition of factor models encompassing both the static factor model - where factors are loaded only contemporaneously - and the Generalised Dynamic Factor Model - where factors are loaded with lags. This decomposition features a new term: the weak common component, defined as the difference between the dynamic and static common components. It is driven by (possibly infinitely many) non-pervasive weak factors which belong to the dynamically common space. Through theoretical and empirical examples - both on U.S. macroeconomic indicators and global financial volatilities - we show that, in general, the weak common component shall not be neglected. Furthermore, we show that, by accounting for the presence of weak common components, we are likely to obtain Impulse Response Functions with more plausible shapes than those obtained from purely static approaches. In addition, we provide consistent estimators for all terms of the canonical decomposition and for the weak factors.
The authors' abstract, as published at the source. Journal of Econometrics, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance