  In order to reach the supply/demand balance, electricity providers need to
predict the demand and production of electricity at different time scales. This
implies the need of modeling weather variables such as temperature, wind speed,
solar radiation and precipitation. This work is dedicated to a new daily
rainfall generator at a single site. It is based on a seasonal hidden Markov
model with mixtures of exponential distributions as emission laws. The
parameters of the exponential distributions include a periodic component in
order to account for the seasonal behaviour of rainfall. We show that under
mild assumptions , the maximum likelihood estimator is strongly consistent,
which is a new result for such models. The model is able to produce arbitrarily
long daily rainfall simulations that reproduce closely different features of
observed time series, including seasonality, rainfall occurrence , daily
distributions of rainfall, dry and rainy spells. The model was fitted and
validated on data from several weather stations across Germany. We show that it
is possible to give a physical interpretation to the estimated states.
