Diagnosing Missing Factors and Time-Varying Factor Effects

Summary

The document considers a monthly return factor model in which one factor explains a substantial share of returns in some periods, but its relationship with returns reverses in others. Pooling the periods yields a lower overall R-squared. This pattern alone does not establish that the factor is robust or that a particular omitted factor is responsible; changing relationships over time are another possible explanation.

The suggested approach is to identify plausible missing factors and include them in the model. Principal component analysis is offered as a starting point, depending on the data and assumptions. The changing direction of the factor’s association also motivates testing time-varying regression coefficients or another method that can represent changing relationships. The note supplies no estimation procedure, validation results, or guidance for distinguishing omitted variables from unstable coefficients, so these proposals are avenues for analysis rather than confirmed diagnoses.

Key ideas

• A strong factor relationship in selected periods can weaken in pooled analysis when its association changes over time.
• A lower pooled R-squared does not by itself prove that an omitted factor is the cause.
• Principal component analysis may help identify additional factors, subject to data and modeling assumptions.
• Time-varying regression coefficients can be considered when factor relationships appear to shift.

Tags

# Missing factor in the factor model


# Missing factor in the factor model












I am developing a factor model to predict monthly returns. One of the factors alone accounts for an R squared of 0.3 to 0.4 for many single periods that has surprised me.

However, for some periods the direction of the factor reverse completely and if I run a single regression for all the periods this factor alone accounts for an R squared of 0.1 which means that the factor is robust but I am missing another factor, correct me if there is another explanation.

Does anyone have any opinion on how to isolate the explanatory power of this factor in the panels in order to eliminate the effect of missing factor or any analytical way to flag the other factor?

## Answer by John (score 3, accepted)

https://quant.stackexchange.com/a/4544

The best option is to identify the other missing factors and include them in your analysis. Depending on your data and assumptions, PCA is a good place to start.

Your data also shows signs of a time-varying correlation with your factor. Hence, it $may$ also be appropriate to allow for time-varying regression coefficients or some other technique to account for this feature of the data.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.