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Hidden Markov models—most often abbreviated to the acronym “HMMs”—are one of the most successful statistical modelling ideas that have came up in the last forty years: the use of hidden (or unobservable) states makes the model generic enough to handle a variety of complex real-world time series, while the relatively simple prior dependence structure (the “Markov” bit) still allows for the use of efficient computational procedures. Our goal with this book is to present a reasonably complete picture of statistical inference for HMMs, from the simplest finite-valued models, which were already studied in the 1960’s, to recent topics like computational aspects of models with continuous state space, asymptotics of maximum likelihood, Bayesian computation and model selection, and all this illustrated with relevant running examples. We want to stress at this point that by using the term hidden Markov model we do not limit …