Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

Apologies if this is not the right place for this question.

I have been digging quite a bit around Kalman Filtering recently and I understand how the base case works. However, I am trying to solve quite a complicated problem using the Kalman filter, but am not sure whether the Kalman Filter can be applied in this context.

I am doing work on UK interest rates and for the data inputs for the analysis I am using Government Spot Rates (government bonds) = C (below), SWAP rates = A (below) and a War Bond Perpetuity = B (below). Now, I have the history of Government bonds (for example) from 01/01/1980 until 31/12/2017. I have the history of the perpetuity from 01/01/1932 until 31/12/2017. I have the history of SWAPs from 01/01/2002 until 31/12/2017. What I am trying to do is to use a Kalman Filter to backfill the SWAP history, so say from 01/01/2002 back to 01/01/1980 using inputs and relationships from the available data that I have described above.

The problem can be described in more simple terms imagining the following:

We have three cars – A, B and C. A is driving on a road in the middle, B is driving on a road above A and C is driving on a road below A (as graph below):

B--------------------------------------------------------------------

A----------------------------------------------------X

C--------------------------------------------------------------------

A simple model to calculate the position of A would be to take the difference between B and C and the difference between A and C so that A = (B-C) – (A-C)

We also know that there is correlation between the movements of the cars (i.e. B is correlated to A, A is correlated to C and C is correlated to B).

I am going to use the observed values I have as my measurement inputs (so A, B and C) which feed into the Kalman Filter algorithm to get my estimated state based on my measurements (so by saying measurements I mean the observed data I have) and my simple equation above (theoretical state) – also introducing some noise around these.

The question I have is what happens when I run out of observations for A and I also loose the relationship between A and C (indicated by the X in the above chart) as the Kalman Filter relies on receiving observations. I have thought of setting the measurement of A to 0 and giving it infinitely big variance, so it gets ignored. So the big questions is - is there a way to use the Kalman Filter to “predicted” where my A will go, given I have lost measurement updates for A at point X (if I was using a GPS for the measurement the GPS has stopped working) but I still know where my B and C are, and I also know the distance between B and C but I have lost the distance between A and C (so my model starts relying on less information)? I was thinking something along the lines of Markov Chain Monte Carlo applying the known correlation structure from before but not sure how this can feed into a Kalman Filter process.

Any thoughts will be much appreciated.

Thanks in advance,

Todor

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Kalman Filtering with missing observations

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**