DLM package in R can model linear space state models of the form: enter image description here

I have a different category of equation which is also a linear polynomial equation of order 1 with constant coefficients. I would like to know if there is any way of modelling this custom set of equations( I want to optimize the parameters using MLE) :

enter image description here enter image description here

Here wt and et are noise parameters with mean 0 and variance 1

As you can see here we have the parameters H and C attached with the noise terms whereas standard DLM has 1 as coefficient to the noise term.Also there is a constant intercept A Is it possible to model it with DLM?

A,B,C are further used to calculate mean and speed of reversion using the below equations, so my main task here is to optimize A,B,C using MLE

enter image description here


1 Answer 1


Parameters $H$ and $C$ simply modify the variance of the respective noises. Since dlm allows for general V and W matrices, I see no problem. You just fit the variances of the noises and then factor out $H$ and $C$ so that the noises have variance 1 if you so wish.

Concerning the intercept $A$, it seems to me that it merely adds a deterministic trend to the state. You might do the same including $A$ as an element of the state vector with variance zero.

  • $\begingroup$ Kindly check the edit to my question, I cannot add A to the state vector because I wish to optimize it along with the other parameters using MLE or EM algorithm. $\endgroup$ Commented Mar 15, 2019 at 16:13
  • $\begingroup$ I think if you add it to the state vector with variance zero, you will get after you run the Kalman filter a value which is its MLE estimate (assuming normality). $\endgroup$
    – F. Tusell
    Commented Mar 15, 2019 at 16:18

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