Empirical forecasting models · Sources
Dynamic factor model sources, papers, and evidence trail
Primary papers, model variants, source notes, and review signals behind the Dynamic factor model page.
References
Primary and official sources
First-party releases, central-bank materials, official statistical agencies, and institutional documents.
[S1] European Central Bank
Doz, Giannone, and Reichlin (2011) 'A Two-Step Estimator for Large Approximate Dynamic Factor Models Based on Kalman Filtering': provided the state-space estimation framework used by the ECB and NY Fed.
Primary - European Central Bank
Academic and research sources
Peer-reviewed papers, books, and research used to ground model mechanisms or contested interpretations.
[S2] Journal of the American Statistical Association
Forecasting Using Principal Components from a Large Number of Predictors
Stock and Watson on factor forecasting.
Academic - Journal of the American Statistical Association - dated 2002
[S3] Econometrica
Determining the Number of Factors in Approximate Factor Models
Bai and Ng on factor-number selection.
Academic - Econometrica - dated 2002
Reference sources
Reference material used for orientation; read primary and academic sources first when claims conflict.
[S4] Reference
Stock and Watson (2002a) 'Forecasting Using Principal Components from a Large Number of Predictors': demonstrated that principal component factors from a large panel improve forecasts of individual macro variables across the board.
Reference
[S5] Reference
Stock and Watson (2002b) 'Macroeconomic Forecasting Using Diffusion Indexes': the companion paper providing the theoretical framework for large-n factor-augmented forecasting.
Reference
[S6] Reference
Bernanke, Boivin, and Eliasz (2005) 'Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach': combined factor extraction with structural VAR identification.
Reference
[S7] Reference
Bai and Ng (2002) 'Determining the Number of Factors in Approximate Factor Models': proposed the IC_p1, IC_p2, IC_p3 criteria for selecting the number of factors.
Reference
Research footing
Evidence and data
Check panel transformations, missing data, factor count, loading stability, and real-time forecast performance.
Calibration or measurement
Factor number, standardization, state dynamics, and release timing determine the signal extracted from the panel.
Boundaries
- Latent factors are rotations, not direct economic objects.
- Structural breaks can move loadings.
- A wide panel does not remove measurement error.
Use guidance
- When sufficient
- Extracting common cyclical signals from a large panel of macro indicators when the object is a low-dimensional summary of real activity, such as a coincident index, a nowcast of quarterly GDP, or a real-activity factor for use in downstream regressions. Stock-Watson 2002 (JBES) diffusion indexes and their state-space extensions are the standard approach when the number of indicators is large but the common variation is concentrated in a few factors.
- When sketch only
- The extracted factor is a statistical object, not a structural shock. It captures whatever the common variation in the panel happens to be, which may conflate demand, supply, and financial shocks unless the panel is structured to isolate one dimension. Do not interpret the factor as a specific causal driver without an additional identification step.
- When to switch
- Switch to a FAVAR (Bernanke-Boivin-Eliasz 2005 QJE) when combining the factor with a small set of explicitly identified structural shocks. Switch to an SVAR (empirical:svar) when the variable count is small enough for direct identification without the dimensionality reduction. Switch to a nowcasting state-space model (empirical:nowcasting) when the goal is real-time tracking that explicitly accounts for the publication calendar.
- Falsification signal
- A factor that explains a small share of common variation across the panel, or that fails to predict the target series out of sample despite a large number of indicators, signals that the factor structure is weak or the panel is too heterogeneous for a low-dimensional factor to summarize it. If the first three factors together account for less than 30 percent of variance in a well-constructed activity panel, the diffusion-index assumption is not supported by the data.
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