Two peas in a pod: Discounting models as a special case of the VARMAX

In this paper, we establish a formal connection between two dynamic modeling approaches that are often taken to study affect dynamics. More specifically, we show that the exponential discounting model can be rewritten to a specific case of the VARMAX, thereby shedding light on the underlying similarities and assumptions of the two models. This derivation has some important consequences for research. First, it allows researchers who use discounting models in their studies to use the tools established within the broader time series literature to evaluate the applicability of their models. Second, it lays bare some of the implicit restrictions discounting models put on their parameters and, therefore, provides a foundation for empirical testing and validation of these models. One of these restrictions concerns the exponential shape of the discounting function that is often assumed in the affect dynamical literature. As an alternative, we briefly introduce the quasi-hyperbolic discounting function.