Dynamic Factor model

Topics: Kalman Filtering, Models
Sep 25, 2014 at 2:49 PM
Hello everyone,

I am trying to use state space model and kalman filter in Iris to extract the unobserved common factors from the time series of 20 variables. They have the same length.
Measurement equations:
CS_? = mu_CS_?+LF1? * CommonFactor1 + LF2? * CommonFactor2 + e?;
Transition equations:
CommonFactor1 = alpha + Beta11 * CommonFactor1{-1} + CommonFactor1_shk;
CommonFactor2= alpha2 + Beta21 * CommonFactor2{-1} + CommonFactor2_shk;

For identifiability I place restrictions on the loadings(on the factors) matrix: LF_i,j =0 for j>i and LF_i,i =1 for i =1,...K.. Another restriction is that the common factors should be uncorrelated with each other.

However, when I estimate the model and extract the common factors, they are correlated.

Please let me know if I should specify the restrictions on the common factor matrix explicitly or if I misuse the Iris state space model for dynamic factor analysis.

Thank you
Kamilla
Marked as answer by jaromirbenes on 9/25/2014 at 8:46 AM
Coordinator
Sep 25, 2014 at 3:45 PM
Hi Kamilla,

Could you post your model files and code? It is not clear from the question what you are trying to do. If ? represents variables 1 through 20 in the expression above, then LF_i,i=1 would only apply to LF11 and LF22 and most of the variables would have no relation to the common factors at all (because j is always greater than i for the equations defining CS_3 through CS_20). I guess I am not following something.

Michael
Coordinator
Sep 25, 2014 at 3:46 PM
Hi Kamilla

This is a general feature of maximum-likelihood filters. The identifying assumptions have most of the time very little in common with the actual estimates, for various reasons. A classic example is the Hodrick-Prescott filter. In its state-space form, the cyclical component (gap) is assumed to be white noise. In 99.9% of economic time series, the estimated HP gap is heavily autocorrelated and far far away from being white noise.

The only solution for you is to write your own estimation procedure that will by design guarantee the uncorrelatedness...

I can't, unfortunately, be of help in this :)

Jaromir
Sep 29, 2014 at 3:02 PM
Michael,

thank you for reply.
yes, you are right.
I used the identification restriction for loadings:
LF_i,j =0 for i>j and LF_i,i =1 for i =1,...K.

Kamilla
Sep 29, 2014 at 3:09 PM
Jaromir,

thank you for reply.
That is what I thought.
In PCA you get uncorrelated factors because the principal components are constructed to be orthogonal.

Kamilla