  Aiming to generate realistic synthetic times series of the bivariate process
of daily mean temperature and precipitations, we introduce a non-homogeneous
hidden Markov model. The non-homogeneity lies in periodic transition
probabilities between the hidden states, and time-dependent emission
distributions. This enables the model to account for the non-stationary
behaviour of weather variables. By carefully choosing the emission
distributions, it is also possible to model the dependance structure between
the two variables. The model is applied to several weather stations in Europe
with various climates, and we show that it is able to simulate realistic
bivariate time series.
