Readings on Autocorrelation Structures?

My student and I are looking to read more about autocorrelation structures in mixed effects models (e.g., accounting for temporal autocorrelations in longitudinal data). We would ultimately be implementing these approaches in brms but want a deeper understanding of the approach in general. Does anyone have any recommended readings on these topics? Could be books, chapters, articles, or blog posts. Thanks!


There’s a bit of discussion in the Stan User’s Guide, but this is a huge area with dozens of different models accounting for varying values, varying variance structure, and even change-point models.

There is a lot of nice work around the INLA project on priors for mixing heterogenous and structured prior (for example, a simple hierarchical prior and a time-series prior, or an AR(1) and AR(2) prior). It’s related to the BYM and BYM2 models for mixing the intrinsic conditional autoregression (ICAR) model with a heterogeneous model. BYM2 uses penalized complexity as outlined here:

Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors.

1 Like

Thanks, bob. Here are a few others I have found:

Mitchell, D. J., Dujon, A. M., Beckmann, C., & Biro, P. A. (2020). Temporal autocorrelation: A neglected factor in the study of behavioral repeatability and plasticity. Behavioral Ecology, 31(1), 222–231.

Zuur, A. F., Ieno, E. N., Walker, N. J., Saveliev, A. A., & Smith, G. M. (2009). Violations of independence—Part I. In Mixed effects models and extensions in ecology with R (pp. 143–160).


These are frequentist treatments but might still be worth taking a look at.

Thompson, Samuel B (2011). “Simple formulas for standard errors that cluster by
both firm and time”. In: Journal of Financial Economics 99.1, pp. 1–10

Petersen, Mitchell A (2009). “Estimating standard errors in finance panel data
sets: Comparing approaches”. In: The Review of Financial Studies 22.1, pp. 435–

Cameron, A Colin, Jonah B Gelbach, and Douglas L Miller (2011). “Robust in-
ference with multiway clustering”. In: Journal of Business & Economic Statistics
29.2, pp. 238–249.

1 Like