MONOCAR (multivariate overlapping noisy observation continuous-time autoregression) is a continuous-time model of time-series data. MONOCAR is aimed at addressing several common complications with time-series data:

Multiple time series
The data are multivariate in nature.
Measurement error
Observations are not perfect measures of the variables of interest but noisy measures of an unobserved underlying process.
Mixed-frequency observations
Each series is regularly spaced but this spacing differs between series.
Irregularly spaced observations
The time from one observation to the next is not constant. This often occurs due to missingness or a lack of an underlying sampling interval.
Noninstantaneous observations
An observation measures an aggregate, such as a sum or average, of a process over an interval of time rather than at an instantaneous point of time.
Overlapping observations
One noninstantaneous observation is a measurement over a time interval that overlaps the measurement time or time interval of another observation.

These features exist in a wide range of time-series data. Two common types of data in political science that include most or all of these features are polling data and events data.

More details on the MONOCAR model, these data complications, and how that model addresses them can be found in the following article:

Tahk, Alexander M. 2015. “A Continuous-Time, Latent-Variable Model of Time-Series Data.” Political Analysis 23 (Spring): 278–298.

The article is available here.

CARMAgeddon is an R package that performs estimation and inference of MONOCAR models. Other continuous-time models may be added to the package in the future. Documentation for the package and examples of its use can be found here. The command to estimate a MONOCAR model is monocar.estimate.


The package can be compiled from source code or installed from a binary package for OS X or Windows. Use of the package requires R, a free software environment for statistical computing and graphics that can be downloaded here. The package also depends on the R packages Rcpp, RcppArmadillo, RcppParallel, and nloptr. All of these packages are available from CRAN.

Installation from binary packages

Users running OS X or Windows can install CARMAgeddon by running install.packages("CARMAgeddon", repos="") from an R prompt. Alternatively, binary packages can be downloaded for OS X here or for Windows here.

Installation from source package

Installation of CARMAgeddon from the source package requires a C++ compiler as well as the R packages mentioned above. Once the prerequisites are installed, the CARMAgeddon package can be installed by running install.packages("CARMAgeddon", repos="", type="source") Alternatively, the source package can be downloaded here.


The CARMAgeddon package was written by Alexander Tahk. For questions about MONOCAR or the CARMAgeddon package, please email the author. Contact information can be found here.