SSMMATLAB: A Set of MATLAB Programs for the Statistical Analysis of State Space Models

Abstract

This article discusses and describes SSMMATLAB, a set of programs written by the author in MATLAB for the statistical analysis of state space models. The state space model considered is very general. It may have univariate or multivariate observations, time-varying system matrices, exogenous inputs, regression effects, incompletely specified initial conditions, such as those that arise with cointegrated VARMA models, and missing values. There are functions to put frequently used models, such as multiplicative VARMA models, VARMAX models in echelon form, cointegrated VARMA models, and univariate structural or ARIMA model-based unobserved components models, into state space form. There are also functions to implement the Hillmer-Tiao canonical decomposition and the smooth trend and cycle estimation proposed by Gómez (2001). Once the model is in state space form, other functions can be used for likelihood evaluation, model estimation, forecasting and smoothing. A set of examples is presented in the SSMMATLAB manual to illustrate the use of these functions.