Estimating a one-factor model using the DLM package

Oops. I see that my "ASCII TeX" depiction of the matrix form got scrambled. Oh well. If you follow the link, you can see the matrix form there.
 
Paul Teetor, Elgin, IL  USA
http://quantdevel.com/public

Hannu,

The MARSS package could solve your problem, but it seems like over-kill for a simple model like this.

I wrote some R code to demonstrate using dlm to fit your model. You can see the code here.

http://bit.ly/spreadModel-dlm

The code fits all three parameters: a, b, and c; plus the variances and initial value.

I did not have much time to test the code, but it seems to run correctly. To use dlm, I
had to put your model into this matrix form:

#                  _    _
#                 |      |
#   y[t] = [a, b] * |   1  | + u[t]
#                 |      |
#                 | s[t] |
#                 |_    _|
#
#  _    _     _    _     _      _     _    _
#   |      |   |      |   |        |   |      |
#   |   1  |   | 1  0 |   |   1    |   |   0  |
#   |      |  =  |      | * |        | + |      |
#   | s[t] |   | 0  c |   | s[t-1] |   | v[t] |
#   |_    _|   |_    _|   |_      _|   |_    _|
#

Good luck. I hope your model works well.

Paul



Paul Teetor, Elgin, IL  USA
http://quantdevel.com/public

I specify the problem more clearly. My model is

y(t) = a + b*s(t) + u(t)
s(t) = c*s(t-1) + v(t)

that is a stochastic linear trend model in the DLM package obtained by
setting dlmModPoly(order = 2). The parameters b and c are fixed to 1 by
construction. In my problem I can allow b = 1, but I would like to estimate
c in the state equation. In other applications, I want to estimate
parameter b in the signal equation, as well.

I have had a look at the MARSS package and it seems that b and c can be
free parameters in estimation.

Hannu

Not sure what you want to do but dlmMLE function would estimate some
parameters to start, and dlmFilter and dlmForecast would predict expected
values. DLM would need some study .
Documents in https://cran.r-project.org/package=dlm are a good start ,
also the book "Dynamic Linear Models with R",  ISBN 978-0-387-77237-0
e-ISBN 978-0-387-77238-7

-----Original Message-----
From: "Hannu Kahra" [hkahra at gmail.com]
Date: 02/05/2017 11:19 AM
To: r-sig-finance at r-project.org
Subject: [R-SIG-Finance] Estimating a one-factor model using the DLM
package

Hi,

I am trying to estimate a one-factor model of the spread y(t) between two
interest rates

y(t) = a + b*s(t) + u(t)
s(t) = c*s(t-1) + v(t)

using the DLM package in R. Is it possible to estimate the parameters a, b,
c, and var(u(t)). Var(v(t)) = 1.

I have EViews code for that and I want to replicate it using R.

Hannu

        [[alternative HTML version deleted]]

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