Many of the proposed models are constructed from two submodels: the first describes rainfall occurrence and the second the rainfall amount on wet days. This chapter decribes the rainfall occurrence and fit Bernoulli–HMMs and Bernoulli–HSMMs to a binary sequence of dry and wet days. It considers a simple model for the daily rainfall series from Zlatograd, namely a two-state Markov chain in which the transition probabilities are allowed to vary seasonally. An alternative dwell-time distribution worth investigating is the shifted negative binomial distribution, which is a natural generalization of the geometric and has two parameters. An advantage of using a dwell-time distribution with a fixed number of parameters is that the model need be fitted only once.