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.
Acknowledgments
This report is released to inform interested parties of research and to encourage discussion. The views expressed on statistical issues are those of the authors and not those of the U.S. Census Bureau. All time series analyzed in this article are from public data sources.
The authors would like to thank the editors and the anonymous referees for their valuable comments and suggestions that improved the quality of the paper
Citation
Anindya Roy. Tucker S. McElroy. "Modeling Extreme Events in Time Series and Their Impact on Seasonal Adjustment in the Post-Covid-19 Era." Bayesian Anal. Advance Publication 1 - 25, 2024. https://doi.org/10.1214/24-BA1424
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