MARSS: Multivariate Autoregressive State-space Models for Analyzing Time-series Data

Abstract

MARSS is a package for fitting multivariate autoregressive state-space models to time-series data. The MARSS package implements state-space models in a maximum likelihood framework. The core functionality of MARSS is based on likelihood maximization using the Kalman filter/smoother, combined with an EM algorithm. To make comparisons with other packages available, parameter estimation is also permitted via direct search routines available in 'optim'. The MARSS package allows data to contain missing values and allows a wide variety of model structures and constraints to be specified (such as fixed or shared parameters). In addition to model-fitting, the package provides bootstrap routines for simulating data and generating confidence intervals, and multiple options for calculating model selection criteria (such as AIC).The MARSS package (Holmes et al., 2012) is an R package for fitting linear multivariate autoregressive state-space (MARSS) models with Gaussian errors to time-series data. This class of model is extremely important in the study of linear stochastic dynamical systems, and these models are used in many different fields, including economics, engineering, genetics, physics and ecology. The model class has different names in different fields; some common names are dynamic linear models (DLMs) and vector autoregressive (VAR) state-space models. There are a number of existing R packages for fitting this class of models, including sspir (Dethlefsen et al., 2009) for univariate data and dlm (Petris, 2010), dse (Gilbert, 2009), KFAS (Helske, 2011) and FKF (Luethi et al., 2012) for multivariate data. Additional packages are available on other platforms, such as SsfPack (Durbin and Koopman, 2001), EViews (www.eviews.com) and Brodgar (www.brodgar.com). Except for Brodgar and sspir, these packages provide maximization of the likelihood surface (for maximum-likelihood parameter estimation) via quasi-Newton or Nelder-Mead type algorithms. The MARSS package was developed to provide an alternative maximization algorithm, based instead on an Expectation-Maximization (EM) algorithm and to provide a standardized modelspecification framework for fitting different model structures.The MARSS package was originally developed for researchers analyzing data in the natural and environmental sciences, because many of the problems often encountered in these fields are not commonly encountered in disciplines like engineering or finance. Two typical problems are high fractions of irregularly spaced missing observations and observation error variance that cannot be estimated or known a priori (Schnute, 1994). Packages developed for other fields did not always allow estimation of the parameters of interest to ecologists because these parameters are always fixed in the package authors' field or application. The MARSS package was developed to address these issues and its three main differences are summarized as follows.First, maximum-likelihood optimization in most packages for fitting state-space models relies on quasi-Newton or Nelde...

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