Statistical software for state space methods

Abstract

In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We rst provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and xed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of di erent estimates for the unobserved state vector: ltering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing condence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models t in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.