Bayesian Inference in Cyclical Component Dynamic Linear Models

1312 Journal of the American Statistical Association, December 1995
identifying a base minimum time interval underlying the
observed times of observations and developing the equally
spaced DLM on that time scale. Then the times with no
observations are treated as points of missing data. This is
important for application. For example, these models are
currently in development as part of a broad study of the
geochemical indicators of climatic change used in the example,
in which raw data series are irregularly spaced (West
1995). Indeed, the timings of observations there are subject
to uncertainties that introduce additional complications that
can be accommodated with further modeling extensions of
obvious utility in other applications (West 1995, sec. 4).
The DLM formulation also permits access to other model
consequences, including predictive aspects. If relevant and
desired in an application, predictions may be routinely generated
from the simulation analysis. For each sampled set
of parameters and subcycles, insert the values into model
(4) and simply project into the future to produce a set of
sampled "futures" of the series. Averaging produces approximate
marginal predictive means and other features of
marginal forecast distributions. But though they are useful
(and traditional), marginal inferences represent crude summaries
of full joint predictive distributions, and other ways
of exploring and summarizing and sets of sequences of such
possible "futures" are needed. This represents an area open
to investigation.
The specific models here are clearly extensible to unrestricted
autoregressive components (Pole and West 1990;
West and Harrison 1989, sec. 9.4) to model stationary cyclical
behavior and additional residual time series structure in
the data, as mentioned in the EEG example. The simulation
framework directly extends to such models, as additive autoregressive
component simply introduce further uncertain
parameters into the system matrix G in (4). Such models
are currently under investigation in specific application contexts.
[Received January 1994. Revised March 1995.]
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