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The Dynamic, the Static, and the Weak: Factor Models and the Analysis of High‐Dimensional Time Series

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  • Matteo Barigozzi
  • Marc Hallin

Abstract

Several fundamental and closely interconnected issues related to factor models are reviewed and discussed: dynamic versus static loadings, rate‐strong versus rate‐weak factors, the concept of weakly common component recently introduced by Gersing, the irrelevance of cross‐sectional ordering and the assumption of cross‐sectional exchangeability, the impact of undetected strong factors, and the problem of combining common and idiosyncratic forecasts. Conclusions all point to the advantages of the General Dynamic Factor Model approach of Forni, Hallin, Lippi, and Reichlin over the widely used Static Approximate Factor Model introduced by Chamberlain and Rothschild.

Suggested Citation

  • Matteo Barigozzi & Marc Hallin, 2026. "The Dynamic, the Static, and the Weak: Factor Models and the Analysis of High‐Dimensional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(1), pages 201-219, January.
    • Handle: RePEc:bla:jtsera:v:47:y:2026:i:1:p:201-219
    DOI: 10.1111/jtsa.12837
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    1. is not listed on IDEAS
    2. Luca Margaritella & Ovidijus Stauskas, 2024. "New Tests of Equal Forecast Accuracy for Factor-Augmented Regressions with Weaker Loadings," Papers 2409.20415, arXiv.org, revised Nov 2025.
    3. Ignacio Garr'on & C. Vladimir Rodr'iguez-Caballero & Esther Ruiz, 2024. "International vulnerability of inflation," Papers 2410.20628, arXiv.org, revised Oct 2024.
    4. Anna Bykhovskaya & Vadim Gorin & Sasha Sodin, 2025. "How weak are weak factors? Uniform inference for signal strength in signal plus noise models," Papers 2507.18554, arXiv.org, revised Feb 2026.
    5. Philipp Gersing, 2024. "Actually, There is No Rotational Indeterminacy in the Approximate Factor Model," Papers 2408.11676, arXiv.org, revised Oct 2024.
    6. Garrón Vedia, Ignacio & Rodríguez Caballero, Carlos Vladimir & Ruiz Ortega, Esther, 2024. "International vulnerability of inflation," DES - Working Papers. Statistics and Econometrics. WS 44814, Universidad Carlos III de Madrid. Departamento de Estadística.

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