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The Kalman filter has been extensively used in Science for various applications, from detecting missile targets to just any changing scenario that can be learned.
I'm trying to understand how Kalman Filter can be applied on Time Series data with Exogenous variables - in a nutshell, trying to replicate PROC UCM in excel.
State-space equation :
To those familiar with the Kalman filter, it essentially consists of the following two steps,
Most of the text on Kalman only introduce univariate analysis, with no exogenous variables. And most applications in control engg seem to suit that as well.
What I'm stuck figuring is -
1. How can I update the H matrix with every observation? Pretty much, MMSE or ML can help me do this, but I'm just unable to do this with just one observation! The problem of recursive estimation with just one observation if I could say...
2. How can I bring in the estimation of betas of other exogenous variables that also affect the Y variable, so, I'm going to be understating the latent state variable to be just a constant base or linear trend.
Any help would be greatly appreciated, and if you have some good docs/sites that explain this better for the econometrician, please do pass it on.
See link for possible suggestions.
This is the document we're currently following and have seemed to make some progress in terms of implementing the Kalman filter in excel!
We're still behind in terms of getting this applied to a econometric model scenario like the Market Mix in Excel, something like replicating the Proc UCM of SAS, which is where some discussion around it can help us understand some bottlenecks faster..!