Hidden Markov models (HMM) are statistical models which can be used to model stochastic processes or time series where the observable values are directly dependent on a sequence of hidden random variables, which usually identify heterogeneous regimes. These models can be homogeneous or non-homogeneous. We apply anon-homogeneous HMM to predict rainfall patterns in Tegucigalpa, Honduras, as a function of other climate covariates and to identify heterogeneous periods of rainfall.We present two procedures for estimating the model, the stochastic EM algorithm and a Bayesian MCMC algorithm, and compare their performance to the most commonly used traditional EM algorithm. We also apply the methods in synthetic datasets and observe that, under tested conditions, the performance of the Bayesian and stochastic EM algorithms is similar. We discuss their slight differences. The EM algorithm presents problems in all studied situations, perhaps because it converged to local solutions. Analysing the Honduras rainfall data set, we identify three heterogeneous rainfall periods and select temperature and humidity as relevant covariates for explaining the transition among these periods.