Chapter 1 Overview

MARSS stands for Multivariate Auto-Regressive(1) State-Space. The MARSS package (Holmes, Ward, and Wills 2012) is an R package for estimating the parameters of linear MARSS models with Gaussian errors. This class of model is extremely important in the study of linear stochastic dynamical systems, and these models are important in many different fields, including economics, engineering, genetics, physics and ecology. The model class has different names in different fields, for example in some fields they are termed dynamic linear models (DLMs) or vector autoregressive (VAR) state-space models.

The MARSS package allows you to easily fit time-varying constrained and unconstrained MARSS models with or without covariates to multivariate time-series data via maximum-likelihood using primarily an EM algorithm (Holmes 2013). The EM algorithm in the MARSS package allows you to apply linear constraints on all the parameters within the model matrices. Fitting via the BFGS algorithm is also provided in the package using R’s optim function, but this is not the focus of the MARSS package.

MARSS, MARSS() and MARSS. MARSS model refers to the class of models which the MARSS package fits using, primarily, an EM algorithm. In the text, MARSS refers to the R package. Within the package, the main fitting function is MARSS(). When the class of model is being discussed, rather than the package or the function, MARSS (not bolded) is used. MAR model refers to a multivariate auto-regressive model while MARSS model refers to a MAR model with the observation (SS) component.