Bayesian Inference for Time Series State Space Models

This article provides a description of time series methods that emphasize modern macroeconomics and finance. It discusses a variety of posterior simulation algorithms and illustrates their use in a range of models. This article introduces the state space framework and explains the main ideas behind filtering, smoothing, and likelihood computation. It also mentions the particle filter as a general approach for estimating state space models and gives a brief discussion of its methods. The particle filter is a very useful tool in the Bayesian analysis of the kinds of complicated nonlinear state space models that are increasingly being used in macroeconomics. It also deals with conditionally Gaussian state space models and non-Gaussian state space models. A discussion of the advantages and disadvantages of each algorithm is provided in this article. This aims to help with the use of these methods in empirical work.