Changing dynamics: Time-varying autoregressive models using generalized additive modeling

Abstract

In psychology, the use of intensive longitudinal data has steeply increased during the past decade. As a result, studying temporal dependencies in such data with autoregressive modeling is becoming common practice. However, standard autoregressive models are often suboptimal as they assume that parameters are time-invariant. This is problematic if changing dynamics (e.g., changes in the temporal dependency of a process) govern the time series. Often a change in the process, such as emotional well-being during therapy, is the very reason why it is interesting and important to study psychological dynamics. As a result, there is a need for an easily applicable method for studying such nonstationary processes that result from changing dynamics. In this article we present such a tool: the semiparametric TV-AR model. We show with a simulation study and an empirical application that the TV-AR model can approximate nonstationary processes well if there are at least 100 time points available and no unknown abrupt changes in the data. Notably, no prior knowledge of the processes that drive change in the dynamic structure is necessary. We conclude that the TV-AR model has significant potential for studying changing dynamics in psychology.