ABSTRACT
This chapter outlines some of the ways in which covariate time series can be incorporated in hidden Markov models (HMMs). Trends and seasonal components, modelled as parametric functions of time, can then be handled as covariates. The chapter describes a number of extensions to the standard HMMs. Covariates can be included in an HMM by allowing some of its parameters to depend on covariates. One can enlarge the class of HMMs by replacing the underlying first-order Markov chain by a higher-order chain. A broad class of models in which the Markov chain is non-homogeneous and which allows for the influence of covariates is that of Hughes. Overparametrization can be circumvented by using some restricted subclass of second-order Markov chain models, for example those of Pegram or those of Raftery. Such models are necessarily less flexible than the general class of second-order Markov chains.
