Learning MARSS

The MARSS R package: https://cran.r-project.org/package=MARSS is part of the Applied Time Series Analysis for Environmental Science suite of software and educational material for time series analysis. See the GitHub repository for the MARSS source code. For fast fitting to large datasets or DFA models, see our companion package, marssTMB.



For Statisticians

For those who work on MARSS models. A good place to start might be the chapter at the end of the User Guide on the comparison of KFAS and MARSS outputs and terminology. Comparing the terminology between the two packages should help understanding the MARSS output. Similarly the chapter on StructTS will help understand the difference in notation and terminology.

MARSS is designed to provide access to every possible conditional expectation of \(\mathbf{X}\) and \(\mathbf{Y}\). “Every possible” means all the temporal conditionings (time 1 to \(t-1\), \(t\) or \(T\)) and all the possible standardizations (none, marginal, Cholesky). It will return the standard errors for all of these combinations. The Residuals subsection in the KFAS chapter will compare the residual options in KFAS to the MARSS residuals. The KFAS terminology may be more familiar and a table in that chapter shows you what terminology is associated with what conditional expectation. Note, KFAS and MARSS give the same values. The difference is notation and terminology.

The EM Derivation paper goes into the nitty-gritty of the underlying EM algorithm. The Residuals paper goes through the Residuals algorithms. All the help files for the functions that implement algorithms have the details for statisticians/developers. My notes on computing the Fisher Information matrix for MARSS are in a series of notes: Notes on computing the Fisher Information matrix for MARSS models I-IV.


If you use MARSS results in publications, please cite the primary citation:

Holmes, E. E., Ward, E. J. and Wills, K. (2012) MARSS: Multivariate Autoregressive State-space Models for Analyzing Time-series Data. The R Journal. 4(1):11-19

You can also cite the package and user guide:

Elizabeth E. Holmes, Eric J. Ward, Mark D. Scheuerell and Kellie Wills (2023). MARSS: Multivariate Autoregressive State-Space Modeling. R package version 3.11.7.

Holmes, E. E., M. D. Scheuerell, and E. J. Ward (“, year,”) Analysis of multivariate time-series using the MARSS package. Version “, meta$Version,”. NOAA Fisheries, Northwest Fisheries Science Center, 2725 Montlake Blvd E., Seattle, WA 98112, DOI: 10.5281/zenodo.5781847

Type citation("MARSS") at the command line to get the most up to data citations.


To see our publications using MARSS models, see the Applied Time Series Analysis website.

NOAA Disclaimer

The MARSS R package is a scientific product and is not official communication of the National Oceanic and Atmospheric Administration, or the United States Department of Commerce. All NOAA code is provided on an ‘as is’ basis and the user assumes responsibility for its use. Any claims against the Department of Commerce or Department of Commerce bureaus stemming from the use of this GitHub project will be governed by all applicable Federal law. Any reference to specific commercial products, processes, or services by service mark, trademark, manufacturer, or otherwise, does not constitute or imply their endorsement, recommendation or favoring by the Department of Commerce. The Department of Commerce seal and logo, or the seal and logo of a DOC bureau, shall not be used in any manner to imply endorsement of any commercial product or activity by DOC or the United States Government.