State-Space Representation/Kalman as an alternative to PCA

[Hector Herrada]

Hi folks, I would like to extract a common factor from the returns of 5 equity indices. With Principal Component Analysis I get my time series of five factors and the corresponding loadings. I was wondering if I could achieve a similar outcome in IRIS. I gave it a try but got an error when estimating the loadings and could not figure out what is wrong. It would be great to have your insight. I have attached my model.

Thank you!

Hector

[Michael Johnston]

Hi Hector, 

Yes I think this is possible. The issue with the model file is that the transition equations block doesn't contain any dynamics. Writing equity1 = equity1 may be a true statement (a tautology even) but basically means that all of your coefficient matrices in the state equation are going to be zeros. If you don't want any persistence in the latent factor that's fine, but you at least need something non-zero in the leading coefficient matrix. E.g., if you write instead

equity1 = a*equity{-1} + shk

then things work. No state space singularity. You can set the AR coefficient to zero if you want, or estimate it. See attached. 

Best,

Mike

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[Hector Herrada]

Hi Mike, thanks for your response. This is fantastic. 

Thanks!

Hector