Informing VAR(1) With Qualitative Dynamical Features Improves Predictive Accuracy

The AR(1) model has been shown to outperform the general VAR(1) model on typical affective time series. Even in combination with a lasso penalty, the reduced VAR(1) model (VAR-lasso) is generally outperformed. A reason for the AR dominance is that the VAR-lasso selects models that are still too complex-the space of all possible VAR models includes simpler models but these are hard to select with a traditional lasso penalty. In this article, we propose a reparametrization of the VAR model by decomposing its transition matrix into a symmetric and antisymmetric component (denoted as SAD), allowing us to construct a hierarchy of meaningful signposts in the VAR model space ranging from simple to complex. The decomposition enables the lasso procedure to pick up qualitatively distinct dynamical features in a more targeted way (like relaxation, shearing, and oscillations); this procedure is called SAD-lasso. This leads to a more intuitive interpretation of the reduced models. By removing the antisymmetric component altogether, we obtain a subclass of symmetric VAR models that form a natural extension of the AR model with the same simple relaxation dynamics but allowing for interactions between the system components. We apply these reparametrized and constrained VAR models to 1,391 psychological time series of affect, and compare their predictive accuracy. This analysis indicates that the SAD-lasso is a better regularization technique than the VAR-lasso. Additionally, the results of an extensive simulation study suggest the existence of symmetric interactions for almost half of the time series considered in this article.

Translational Abstract The inclusion of lagged interactions between the variables of interest in an autoregressive model has been shown typically not to improve the description of psychological time series. To many researchers in the field, this finding is counterintuitive because psychological systems, like the affect system, are generally conceived as complicated systems with constituents that are (at least partly) interacting. However, simultaneously including all possible interactions leads to an overly complex model that produces worse predictions. Regrettably, the commonly used method to systematically limit the number of possible interactions, lasso, does not significantly improve predictions. In this article, a taxonomy is provided of all possible dynamical behaviors encompassed by the autoregressive model (exponential relaxation, shearing, and oscillations). By adjusting the lasso procedure to directly target each of these behaviors, the prediction can be significantly improved and lagged interactions can better be detected. Additionally, we find that exponential relaxation dynamics is the most prominent dynamical behavior in time series of affect.