# Time-varying parameter Kalman filter

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steve on 3 Jan 2014
Answered: John Petersen on 4 Jan 2014
Hello,
I can't seem to find any good explanation or matlab implementation of a time-varying parameter Kalman filter.
I'm looking to estimate a time-varying coefficient model - I see this done in econometrics literature a fair bit but can find almost nothing written about it for matlab - I have found an example in R.
For example, the matlab helpguide to Kalman filtering (<http://www.mathworks.co.uk/help/control/ug/kalman-filtering.html#f0-1003572 here>) claims that it is possible to use implement a time-varying design but then provides an example in which the same time-invariant parameter matrices are used.
If I wanted to have a a time-dependent matrix C (same notation as mathworks example) what would I do? As an alternative to a regression (or rolling regression) I want to estimate a time-varying beta in the equation y(t) = C(t)*B(t). I'd have a state equation B(t) = B(t-1) + w(t).
Can anyone point me to a good example of how this is done?
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### Answers (1)

John Petersen on 4 Jan 2014
If your equations are linear then you can use the regular Kalman filter equations. Just put time (or delta time) where you need them in the matrix elements. If this isn't enough information, list your state and measurement equations or a simplified(or subset) version of them and I or someone else can help you. If your equations are nonlinear then you will need to use the Extended Kalman equations or unscented.
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