Common mistake 1 with Dynamic factor model

Not standardising. A series in rupees and a series in percent cannot be combined meaningfully at raw scale.

Common mistake 2 with Dynamic factor model

Naming the factor and then treating the name as a finding. It is a weighted average of your inputs, and it means what those inputs mean.

Common mistake 3 with Dynamic factor model

Adding factors until the fit is good. Each extra factor is harder to interpret and the later ones are usually noise.

Common mistake 4 with Dynamic factor model

Using it on a handful of series. Factor models are asymptotic in the number of series as well as the number of periods; with three series the factor is barely distinguishable from the first principal component.

EconStatsCraft › Dynamic factor model

Dynamic factor model

When twenty indicators all move with the business cycle, the cycle is what you want - not twenty separate models. Extracts the common factor driving a set of series and reports how strongly each one loads on it.

What it needs

Series - Three or more series you believe share a common driver.

The intuition

Two hundred macroeconomic series do not contain two hundred independent pieces of news. Most of them move together because a handful of forces - the business cycle, an oil price, a monetary shock - drive them all. A dynamic factor model estimates those few unobserved forces from the whole panel, which is how a nowcast can use hundreds of indicators without any of the multicollinearity that would destroy a regression.

When to use it

When many indicators move together and you want the common movement itself - a business-cycle index, a financial conditions index - or when you want to forecast using many predictors without estimating a coefficient for each.

Where the estimator comes from

The model is x_{it}=\lambda_i'f_t+e_{it} with f_t a small vector of common factors following their own VAR, f_t=A_1f_{t-1}+\dots+u_t, and e_{it} idiosyncratic. Two estimation routes exist. Principal components on the standardised panel is consistent as both N and T grow (Stock and Watson, 2002) and needs no distributional assumption; it is fast and handles hundreds of series. The state-space route puts the model in Kalman filter form and estimates by maximum likelihood, which is slower but handles MISSING DATA and mixed frequencies naturally - the filter simply skips an unobserved measurement - which is why nowcasting uses it.

The model

x_{it}=\lambda_i' f_t+e_{it},\qquad f_t=A_1f_{t-1}+\cdots+A_pf_{t-p}+u_t

What it assumes

The idiosyncratic components are mutually uncorrelated - that is what makes a factor "common".
The series are standardised, or at least on comparable scales; otherwise the largest-variance series dominates.
The number of factors is chosen by you. Information criteria exist but are sensitive.
The panel is wide enough for the factors to be identified. Factor estimates improve with the number of SERIES, not just the number of periods, and a handful of series cannot pin down a common factor.

Statistical properties

Factors are identified only up to rotation, exactly as in factor analysis. Any invertible transformation of the factors with the inverse applied to the loadings fits identically, so the individual factors have no inherent meaning until normalised.
The number of factors is chosen by an information criterion designed for this setting - Bai and Ng (2002) - rather than by a scree plot, because the usual criteria do not account for both N and T growing.
The Kalman filter handles ragged edges: series published at different lags leave the end of the panel jagged, and the filter fills them without ad hoc interpolation. This is the single feature that makes nowcasting practical.
Standardisation is essential. Series in different units contribute variance in proportion to their scale, and an unstandardised panel yields factors that track whichever series is measured in the largest numbers.
Common factors explain the CO-movement, not the level of any one series. A high factor R-squared for GDP does not mean the model forecasts GDP well.
The idiosyncratic components are assumed weakly correlated across series. Strong local correlation - all the housing series moving together for housing reasons - produces a spurious extra factor.

How to read the output

Loadings say how strongly each series moves with each factor. Near zero means that series marches to its own drum and adds little.
The SIGN of a factor is arbitrary - flip the factor and every loading with it and nothing changes. Never interpret a sign alone.
Plot the factor against dates you know. If it dips in the downturns you can name, it is capturing the cycle.
The share of variance explained by the first factor is the headline diagnostic. If it is low, the series do not have much in common and the factor is a weighted average rather than a driver.

A worked reading

A panel of macro indicators where the first two factors explain most of the co-movement. The useful diagnostic is the loading pattern rather than the factors themselves: if the first factor loads positively on every output and employment series and negatively on unemployment, it is a business cycle whatever the algebra calls it. And when a new month of industrial production arrives, the nowcast moves - that movement is the news content of the release, isolated from everything already known, which is exactly what a policymaker wants and what no single-equation regression on a ragged panel can deliver.

Symptom → diagnosis → what to do

If you see this	It means	Do this
First factor tracking one series	Unstandardised panel, or that series dominates	Standardise; check the loadings
Bai-Ng suggesting many more factors than the scree	Normal; the criteria differ	Prefer Bai-Ng, which is designed for this asymptotic
A factor loading only on one group	A local factor, not a common one	Consider removing that block or modelling it separately
Nowcast jumping when a series is released	The intended behaviour	The revision IS the news content of that release
Kalman filter not converging	Too many factors or too little data	Reduce the factor count
Factors uninterpretable	They are only identified up to rotation	Normalise, or interpret the space rather than the axes

Common mistakes

Not standardising. A series in rupees and a series in percent cannot be combined meaningfully at raw scale.
Naming the factor and then treating the name as a finding. It is a weighted average of your inputs, and it means what those inputs mean.
Adding factors until the fit is good. Each extra factor is harder to interpret and the later ones are usually noise.
Using it on a handful of series. Factor models are asymptotic in the number of series as well as the number of periods; with three series the factor is barely distinguishable from the first principal component.

Where to read this properly

Stock and Watson (2002), "Forecasting Using Principal Components", JASA 97(460).
Bai and Ng (2002), "Determining the Number of Factors in Approximate Factor Models", Econometrica 70(1).
Giannone, Reichlin and Small (2008), "Nowcasting", Journal of Monetary Economics 55(4).
Doz, Giannone and Reichlin (2012), Review of Economics and Statistics 94(4).

Related Time series - several series

Yield curve (Nelson–Siegel / Svensson) · Dynamic regression (ARIMAX) · Structural VAR · VAR · Granger causality · Cointegration · VECM · ARDL & bounds test

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Dynamic factor model

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

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