Taking Variance Seriously: Visualizing the Statistical and Substantive Significance of ARCH-GARCH Models

Autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models allow users to estimate the conditional mean and conditional error variance of a time series process. Although simulation methods exist to disaggregate the short- and long-run effects of covariate shocks to the conditional mean, scholars’ inferences about the conditional error variance are currently limited to tabular interpretation. We propose a novel method of interpretation that moves beyond these tabular inferences. First, we show how changes in ARCH-GARCH processes are conditional on starting values, other covariates, and dynamics, which has led to incomplete or even incorrect inferences. We then develop three bootstrapping techniques to simulate conditional error variance model results and showcase the usefulness of each through replication of prominent studies. Our techniques demonstrate the crucial role of simulation and prediction for drawing statistical and substantive inferences about the volatility of dynamic time series processes.