SSMMATLAB: A Set ofMATLABPrograms 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.

Supply chain decision support systems based on a novel hierarchical forecasting approach

“…This toolbox is based on several references, like Harvey (1989), Young et al (1999), Durbin and Koopman (2012), Casals et al (2016). Other pieces of software related to this are, among many others, Commandeur et al 2011, Koopman et al (2009), Taylor et al (2007), Gómez (2015).…”

A Set of State–Space Models at a High Disaggregation Level to Forecast Italian Industrial Production

“…Once the Italian and German data are loaded in memory, the automatic identification procedure stores the results about their respective state-space forms. If the algorithms crashes, it is mandatory to use the logarithmic transformation (see Gómez [15]) and the property of log normal distribution to bring those data on the original level if it is desirable. Finally, the matrices are cast on the main diagonal of F t u , G t u , X t u , H t u , and J t u .…”

“…Equation (A1) is cast in state-space form to backcast daily consumption data in the remote past. The equation is a univariate autoregressive model over weekly frequencies with a set of exogenous regressors composed of weekly seasonal log differences daily data of natural gas for thermoelectric use and by a year fixed seasonal cycle over a year (see Gómez [15]).…”

SSpace: A Toolbox for State Space Modeling

“…A partial review is available in Volume 41 of the Journal of Statistical Software (Commandeur, Koopman, and Ooms 2011). There are several toolboxes written in MATLAB, like toolboxes supplied with the core program, but also CAPTAIN (Taylor et al 2007), SSM (Peng and Aston 2011), SSMMATLAB (Gómez 2015) and E4 (Casals, Garcia-Hiernaux, Jerez, Sotoca, and Trindade 2016). One piece of software widely known is SSfPack (Koopman, Shephard, and Doornik 2008).…”