Time Series Analysis by State Space Methods, 2nd Edition

This book presents a comprehensive treatment of the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as being made up of distinct components such as trend, seasonal, regression elements and disturbance elements, each of which is modelled separately. The techniques that emerge from this approach are very flexible.

Part I presents a full treatment of the construction and analysis of linear Gaussian state space models. The methods are based on the Kalman filter and are appropriate for a wide range of problems in practical time series analysis. The analysis can be carried out from both classical and Bayesian perspectives. Part I then presents illustrations to real series and exercises are provided for a selection of chapters.

Part II discusses approximate and exact approaches for handling broad classes of non-Gaussian and nonlinear state space models. Approximate methods include the extended Kalman filter and the more recently developed unscented Kalman filter. The book shows that exact treatments become feasible when simulation-based methods such as importance sampling and particle filtering are adopted. Bayesian treatments based on simulation methods are also explored.