What goes up must come down: Theory and model specification of threshold dynamics

Abstract

Objectives Despite the frequent use of time series models in the social sciences, they have often remained within the confines of assuming purely linear dynamic effects. We contend that many theories involve relationships that are inherently non-linear. Methods We discuss several approaches to modeling a variety of these types of non-linear autoregressive data-generating processes, specifically threshold effects. Results We replicate and extend a recent analysis, and show evidence of threshold processes. Conclusion In doing so, we show that threshold models allow us to test richer, more complex theoretical implications about dynamic effects.