A Tutorial on Estimating Time-Varying Vector Autoregressive Models

TL;DR

This paper introduces methods for estimating time-varying Vector Autoregressive models in psychological research, using splines and kernel-smoothing, with practical guidance and simulation evaluations.

Contribution

It provides a comprehensive tutorial on estimating and applying time-varying VAR models, including methods, simulations, and step-by-step application guidance.

Findings

Spline and kernel-smoothing methods perform well in typical scenarios.

Regularization improves estimation accuracy in complex models.

The tutorial demonstrates practical application on real data.

Abstract

Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences from between-subjects data, and naturally address heterogeneity between subjects. A popular model for these data is the Vector Autoregressive (VAR) model, in which each variable is predicted as a linear function of all variables at previous time points. A key assumption of this model is that its parameters are constant (or stationary) across time. However, in many areas of psychological research time-varying parameters are plausible or even the subject of study. In this tutorial paper, we introduce methods to estimate time-varying VAR models based on splines and kernel-smoothing with/without regularization. We use simulations to evaluate the relative performance of all methods in scenarios typical in applied research, and discuss their strengths and weaknesses. Finally, we provide a step-by-step tutorial showing how to apply the discussed methods to an openly available time series of mood-related measurements.