  We consider the problem of modeling discrete-valued vector time series data
using extensions of Chow-Liu tree models to capture both dependencies across
time and dependencies across variables. Conditional Chow-Liu tree models are
introduced, as an extension to standard Chow-Liu trees, for modeling
conditional rather than joint densities. We describe learning algorithms for
such models and show how they can be used to learn parsimonious representations
for the output distributions in hidden Markov models. These models are applied
to the important problem of simulating and forecasting daily precipitation
occurrence for networks of rain stations. To demonstrate the effectiveness of
the models, we compare their performance versus a number of alternatives using
historical precipitation data from Southwestern Australia and the Western
United States. We illustrate how the structure and parameters of the models can
be used to provide an improved meteorological interpretation of such data.
