Hidden Markov models are extensions of Markov models where each observation is the result of a stochastic process in one of several unobserved states. Though favored by many scientists because of its unique and applicable mathematical structure, its independence assumption between the consecutive observations hampered further application. Autoregressive hidden Markov model is a combination of autoregressive time series and hidden Markov chains. Observations are generated by a few autoregressive time series while the switches between each autoregressive time series are controlled by a hidden Markov chain. In this thesis, we present the basic concepts, theory and associated approaches and algorithms for hidden Markov models, time series and autoregressive hidden Markov models. We have also built a bivariate autoregressive hidden Markov model on the temperature data from the Pacific Ocean to understand the mechanism of El Nino. The parameters and the state path of the model are estimated through the Segmental K-mean algorithm and the state estimations of the autoregressive hidden Markov model have been compared with the estimations from a conventional hidden Markov model. Overall, the results confirm the strength of the autoregressive hidden Markov models in the El Nino study and the research sets an example of ARHMM's application in the meteorology.

Hidden Markov models are extensions of Markov models where each observation is the result of a stochastic process in one of several unobserved states. Though favored by many scientists because of its unique and applicable mathematical structure, its independence assumption between the consecutive observations hampered further application. Autoregressive hidden Markov model is a combination of autoregressive time series and hidden Markov chains. Observations are generated by a few autoregressive time series while the switches between each autoregressive time series are controlled by a hidden Markov chain. In this thesis, we present the basic concepts, theory and associated approaches and algorithms for hidden Markov models, time series and autoregressive hidden Markov models. We have also built a bivariate autoregressive hidden Markov model on the temperature data from the Pacific Ocean to understand the mechanism of El Nino. The parameters and the state path of the model are estimated through the Segmental K-mean algorithm and the state estimations of the autoregressive hidden Markov model have been compared with the estimations from a conventional hidden Markov model. Overall, the results confirm the strength of the autoregressive hidden Markov models in the El Nino study and the research sets an example of ARHMM's application in the meteorology.