# [R] Dynamic Linear Models for Times Series - Implemented?

Gavin Simpson gavin.simpson at ucl.ac.uk
Wed Feb 12 14:16:03 CET 2003

```Hi,

Following an off-list reply to my original post, I realised that I hadn't
really provided very much information for you to work with.  So here's a
second attempt:

Following West & Harrison (1989) and Pole et al. (1994) a DLM is defined as:

Y[t] = F'[t]theta[t] + v[t],	v[t] ~ N[0,V] #Observation equation
theta[t] = G[t]theta[t-1] + w[t],  w[t] ~ N[0,W] #system equation

The system equation is a first order Markov process, where G[t] is a matrix
of known coefficients that defines the systematic evolution of the state
vector (theta[t]) across time, and w[t] is an unobservable stochastic error
term having a normal distribution with zero mean and covariance matrix.

Y[t] denotes the observation series at time t
F[t] is a vector of known constants (the regression vector)
theta[t] denotes the vector of model state parameters
v[t] is a stochastic error term having zero mean and variance V[t]

If I have understood Brockwell and Davis (1991) correctly, the DLM can be
considered from the point of view of State-space models (although I am
venturing some way out of my statistical depth here, all the papers I have
collected are applied examples and they all refer to dynamic Linear Models,
not State-space models).

It seems that some of this has been done in S (for S-Plus), as I found the
bts package by Harrison and Reed on StatLib
(http://lib.stat.cmu.edu/DOS/S/),

"SPLUS for Windows functions and datasets for Bayesian forecasting based on
the algorithms in Bayesian Forecasting and Dynamic Linear Models by West and
Harrison"

So I was wondering whether anyone knew of existing R code that could fit
such models?

Many thanks

Gavin Simpson

Refs:
Brockwell and Davis (1991).  Time Series: Theory and Methods.  Springer
Pole, West and Harrison (1994).  Applied Bayesian Forecasting and Time
Series Analysis.  Chapman & Hall/CRC
West and Harrison (1989).  Bayesian Forecasting and Dynamic Models.
Springer

-----Original Message-----
On Behalf Of Gavin Simpson
Sent: 11 February 2003 17:49
To: r-help
Subject: [R] Dynamic Linear Models for Times Series - Implemented?

Hi,

I was wondering whether a package that can perform dynamic linear models on
times series data was available for R?

Many Thanks,

Gavin Simpson

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Gavin Simpson                     [T] +44 (0)20 7679 5522
ENSIS Research Fellow             [F] +44 (0)20 7679 7565
ENSIS Ltd. & ECRC                 [E] gavin.simpson at ucl.ac.uk
UCL Department of Geography
26 Bedford Way
London.  WC1H 0AP.
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