Markov Models for Count Time Series
Richard Arnold Davis, William T. M. Dunsmuir · 2016
The family of linear state-space models (SSM), which have been a staple in the time series literature for the past 70 plus years, provides a flexible modeling framework that is applicable to a wide range of time series. The popularity of these models stems in large part from the development of the Kalman recursions, which provides a quick updating scheme for predicting, filtering, and smoothing a time series. In addition, many of the commonly used time series models, such as univariate and multivariate ARMA and ARIMA processes can be embedded in an SSM, and as such can take advantage of fast recursive calculation related to prediction and filtering afforded by the Kalman recursions. Recent accounts of linear state space models can be found in Brockwell and Davis (1991) , Brockwell and Davis (2002) , Durbin and Koopman (2012) , and Shumway and Stoffer (2011) .