Linear Regression with Stationary Errors: the R Package slm

This paper introduces the R package slm, which stands for Stationary Linear Models. The package contains a set of statistical procedures for linear regression in the general context where the error process is strictly stationary with a short memory. We work in the setting of (Hannan 1973), who proved the asymptotic normality of the (normalized) least squares estimators (LSE) under very mild conditions on the error process. We propose different ways to estimate the asymptotic covariance matrix of the LSE and then to correct the type I error rates of the usual tests on the parameters (as well as confidence intervals). The procedures are evaluated through different sets of simulations.

Emmanuel Caron (Laboratoire de Mathématiques d’Avignon EA2151) , Jérôme Dedecker (Laboratoire MAP5 UMR 8145) , Bertrand Michel (Laboratoire de Mathématiques Jean Leray UMR 6629)

Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at

E. J. Hannan. Central limit theorems for time series regression. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 26(2): 157–170, 1973.



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

Caron, et al., "Linear Regression with Stationary Errors: the R Package slm", The R Journal, 2021

BibTeX citation

  author = {Caron, Emmanuel and Dedecker, Jérôme and Michel, Bertrand},
  title = {Linear Regression with Stationary Errors: the R Package slm},
  journal = {The R Journal},
  year = {2021},
  note = {},
  doi = {10.32614/RJ-2021-030},
  volume = {13},
  issue = {1},
  issn = {2073-4859},
  pages = {146-163}