Model checking for vector autoregressive models

Time series data have become pervasive in psychological science and vector autoregressive (VAR) models are now widely used to study within-person dynamics. However, researchers rarely check systematically whether these models fit 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. This tutorial 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. We provide code for extracting predictions and residuals from popular software packages and introduce the new R package VARcheck, which generates diagnostic plots with only a few lines of code. We apply these tools in a realistic setting by performing model checks for a multilevel VAR model estimated from emotion measurements from 179 people over 3 weeks. Finally, we discuss three ways in which model checking can advance psychological time series research: improving measurement, building better statistical models, and supporting theory development. (PsycInfo Database Record (c) 2026 APA, all rights reserved).