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

Wed Feb 12 17:22:04 CET 2003

```Gavin

I am not familiar with the two texts you mention that define DLM, but I think
since at least twenty years prior to those texts, the term has been used to mean
the state-space model you describe, and also ARMA models, transfer function
models, and possibly some other representations of linear models in time series
(and continuous time too, which is not always consider time series).

There are several packages on CRAN that implement ARMA and/or state-space
models, including my dse (Dynamic Systems Estimation) which handles both
multivariate ARMA and the state-space model you describe. For estimation
purposes I would suggest you consider the innovations form state-space model
rather than the non-innovations form you have indicated. If you use the
non-innovations form you will need to worry much more about identification
problems.

Paul Gilbert

Gavin Simpson wrote:
>
> 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
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