Hidden Markov models with binary dependence

Hidden Markov models are widely used to model the probabilistic structures with latent variables. The main assumption of hidden Markov models is that; observation symbols are conditionally independent and identically distributed random variables. There exist some cases where this assumption may not be valid in practice. That is, an observation symbol that occurs in the current state may depend on the previous observation symbol that occurred in the previous state. In this study, a new type of hidden Markov model is introduced in which the current pair of hidden state-emitted observation symbol and the previous pair of those have a first-order Markov dependency. The proposed model is capable of capturing a possible first-order Markov dependency between the last and the previous steps of the system. In addition, it provides a better representation for the appropriate real-life problems where, if the observation symbols have conditional dependence. It is an alternative model to the classical hidden Markov model for revealing the Markov dependency between the current and the previous binary information of the system. An experimental study is conducted to show the performance of the proposed model compared to the classical hidden Markov model. Besides, two different case studies are conducted namely the occurrences of strong earthquakes and daily stock prices are modeled with both the classical hidden Markov model and the proposed model, and the results are compared. •A binary-dependent HMM which uses more information from the past is proposed.•The distribution of the current information depends on the previous information.•Baum–Welch​ and Viterbi algorithms are modified based on the assumptions.•The dependence between the current and the previous information can be revealed.•Two case studies are presented to support the justification of the model.