Nonlinear Kalman Filter: Theoretical Background

Topics: Kalman Filtering
Jul 28, 2015 at 9:41 AM
Greetings!

I was wondering what algorithm lies behind the exact nonlinear Kalman filtering employed in IRIS. Is it based on some kind of linearisation of nonlinear equations invlolved?

Best,
AndreyO
Coordinator
Jul 28, 2015 at 6:39 PM
As far as I know it is able to take a non-linear prediction step but the MSE matrices etc. are still based on assumptions about linearity and Gaussian shocks as in the standard Kalman filter. In this sense it may not be optimal if the non-linearities are strong.

People like Robert Kollmann have developed analytic filtering solutions to which are second-order accurate: http://www.robertkollmann.com/KOLLMANN_PUBL_COMPUT_ECON_2015.pdf. Otherwise you need to use a particle filter (unless I have missed some recent paper in the literature...).

Jaromir wrote the code behind this. Perhaps he can comment with more detail.
Marked as answer by jaromirbenes on 7/28/2015 at 10:41 AM
Coordinator
Jul 28, 2015 at 6:45 PM
Yes, as Michael said... The nonlinear Kalman filter in IRIS only runs a nonlinear prediction step, while the updating(filtering) and smoothing steps are the usual first order algorithms. This a quick-and-dirty approach that can capture a substantial portion of nonlinear behavior in many model, but may fail when the nonlinearities are more non-trivial...

Best,
Jaromir
Marked as answer by jaromirbenes on 7/28/2015 at 10:45 AM
Jul 29, 2015 at 9:24 AM
Thanks for the replies!
Could you give a hint on how the nonlinear prediction step is computed?

Best,
AndreyO
Coordinator
Jul 29, 2015 at 9:27 AM
Hi Andrey

It is computed using the equation-selective nonlinear algorithm, the same as nonlinear simulations in the simulate(...) command. I'll post a note describing the algorithm on the website.
Marked as answer by jaromirbenes on 7/29/2015 at 1:27 AM
Jul 29, 2015 at 9:36 AM
Thank you, Jaromir!