Title: Bayesian Vector Autoregressive Models for Structure and Parameter
Learning

Author: Fabian Dablander

Affiliation: University of Amsterdam

Abstract:
The Vector Autoregressive (VAR) model has become a popular choice for modeling
time-series of individual subjects in Psychology. The number of observations
in typical psychological applications is often small, however, putting the
reliability of VAR coefficients into question. Recently, Bulteel et al. (2018)
suggested to forgo estimating the off-diagonal elements in the VAR model,
i.e., to fit an AR model instead. Within this context, my talk has two parts.
First, I will discuss the relative performance of the AR and VAR model with a
simulation study, illustrating the bias-variance trade-off. Second, I will
argue that it is preferable to test the nullity of off-diagonal elements
individually instead of jointly. The Bayesian VAR model with a spike-and-slab
prior provides an elegant way to achieve this, yielding a posterior
distribution over all possible graphs (structure learning) and thus Bayes
factors for individual edges. I will discuss this model's relation to other
(continuous) shrinkage methods such as the regularized horseshoe, and assess
its relative performance in an extensive simulation study. I will conclude by
applying the model to data sets from Psychology and Economics. The methods
will be made available in the R package BayesVAR.


References:
Bulteel, K., Mestdagh, M., Tuerlinckx, F., & Ceulemans, E. (2018). VAR (1)
based models do not always outpredict AR (1) models in typical psychological
applications. Psychological methods, 23(4), 740-756.