Mixed memory Markov models for time series analysis

The paper presents a method for analyzing coupled time series using Markov models in a domain where the state space is immense. To make the parameter estimation tractable, the large state space is represented as the Cartesian product of smaller state spaces, a paradigm known as factorial Markov models. The transition matrix for this model is represented as a mixture of the transition matrices of the underlying dynamical processes. This formulation is know as mixed memory Markov models. Using this framework, the author analyzes the daily exchange rates for five currencies-British pound, Canadian dollar, Deutschmark, Japanese yen, and Swiss franc-as measured against the US dollar