Modeling Extreme Events in Time Series and Their Impact on Seasonal Adjustment in the Post-Covid-19 Era

Abstract

A conventional approach to the extraction of latent components in a time series is to first model extreme values (including level shifts and seasonal outliers) as fixed effects, followed by their removal. Then the extreme-value adjusted series can be filtered using linear (Gaussian) techniques. A drawback is that identification of the epochs of extreme values is needed, and the uncertainty about this identification – as well as the removal of extremes – goes unmeasured. Alternatively, each outlier effect can be modeled as a particular type of latent stochastic process driven by heavy-tailed innovations; extraction of latent components then follows non-linear techniques and does not require identification of extreme epochs. We model monthly retail data impacted by the Covid-19 epidemic by incorporating additive outliers and level shifts as heavy-tailed latent processes, and estimate the unknown parameters through a Bayesian approach that utilizes Gibbs sampling. As a result, we can extract retail trends that incorporate stochastic level shifts and a full measure of the extraction uncertainty. An added benefit of the proposed approach is an estimate of a counterfactual trend following an extreme event. The posterior estimate of the counterfactual trend can be used to quantify the impact of an extreme event.