Model Checking for Vector Autoregressive Models

Time series have become pervasive in psychological science, and Vector Autoregressive (VAR) models are now among the most popular tools for studying within-person dynamics in such data. However, researchers rarely check systematically how well a VAR model fits their data. This is problematic because model misfit can lead both to incorrect interpretations of model parameters and to missed structure in the data that would be theoretically interesting. We provide a tutorial that explains the theory behind model checking, discusses the most common types of VAR model misspecification in psychological time series, and introduces diagnostics for detecting them using plots and simulations. In addition, we provide code to extract predictions and residuals from popular software packages, along with the new R-package VARcheck, which allows researchers to create extensive diagnostic plots with only a few lines of code. We then apply these tools to assess the fit of a multilevel VAR model estimated on a typical empirical dataset of emotion measurements from 179 people over three weeks. We conclude by discussing three complementary ways in which model checking can advance psychological science using time series.