spGARCH: An R-Package for Spatial and Spatiotemporal ARCH and GARCH models

In this paper, a general overview on spatial and spatiotemporal ARCH models is provided. In particular, we distinguish between three different spatial ARCH-type models. In addition to the original definition of ?, we introduce an logarithmic spatial ARCH model in this paper. For this new model, maximum-likelihood estimators for the parameters are proposed. In addition, we consider a new complex-valued definition of the spatial ARCH process. Moreover, spatial GARCH models are briefly discussed. From a practical point of view, the use of the R-package spGARCH is demonstrated. To be precise, we show how the proposed spatial ARCH models can be simulated and summarize the variety of spatial models, which can be estimated by the estimation functions provided in the package. Eventually, we apply all procedures to a real-data example.

Philipp Otto

CRAN packages used

spGARCH, spdep, gstat, Stem, rugarch, Rsolnp, Rcpp, RcppEigen

CRAN Task Views implied by cited packages

Spatial, NumericalMathematics, SpatioTemporal, Finance, HighPerformanceComputing, Optimization, TimeSeries


Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".


For attribution, please cite this work as

Otto, "spGARCH: An R-Package for Spatial and Spatiotemporal ARCH and GARCH models", The R Journal, 2019

BibTeX citation

  author = {Otto, Philipp},
  title = {spGARCH: An R-Package for Spatial and Spatiotemporal ARCH and GARCH models},
  journal = {The R Journal},
  year = {2019},
  note = {https://doi.org/10.32614/RJ-2019-053},
  doi = {10.32614/RJ-2019-053},
  volume = {11},
  issue = {2},
  issn = {2073-4859},
  pages = {401-420}