This chapter presents an analysis of a series of long and short eruption durations of the geyser, univariate models for the series of durations and waiting times, in their original, non-dichotomized, form; and a bivariate model for the durations and waiting times. Although it is true that the second-order Markov chain seems a slightly better model on the basis of the model selection exercise, and possibly on the basis of the autocorrelation function, both are reasonable models capable of describing the principal features of the data without using an excessive number of parameters. The hidden Markov models (HMM) perhaps has the advantage of relative simplicity, given its nature as a Markov chain with some noise in one of the states. The ratio of likelihoods can be used to provide the forecasts implied by the fitted two-state HMM.