A New Frontier for Studying Within-Person Variability: Bayesian Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models

Abstract

Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on the within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified DCC model that accommodate external time-varying predictors for the within-person variance. This main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, three components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. Moreover, these models allow for variance spill-over effects from one time-series to another. We illustrate the pdBEKK-and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance.Overall, the pdBEKK seems to result in a more straight forward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect non-zero parameters. Potentials and limitations are discussed. We provide an R-package bmgarch that facilitates the estimation of these types of models.

Bayesian Multivariate GARCH Models for Within-Person Variance Forecasting

“…As outlined in the introduction, models that forecast volatility are fundamental in econometrics, and they can be reparameterized in a way that one can interpret their parameters in a behavioral context (Rast et al, 2020). First and foremost, however, MGARCH models are being developed with mainly one goal in mind: to forecast the volatility and variance spill overs in multivariate time-series (Bauwens et al, 2006).…”

“…These individuals will be referred to as Individual 1 and Individual 2. All models were estimated using the bmgarch 1 package in R. All prior specifications are described in detail elsewhere (Rast et al, 2020).…”