Modeling Extreme Events in Time Series and Their Impact on Seasonal Adjustment in the Post-Covid-19 Era.
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| Title: | Modeling Extreme Events in Time Series and Their Impact on Seasonal Adjustment in the Post-Covid-19 Era. |
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| Authors: | Roy, Anindya, McElroy, Tucker S. |
| Source: | Bayesian Analysis; Sep2025, Vol. 20 Issue 3, p1057-1081, 25p |
| Subject Terms: | GIBBS sampling, TIME series analysis, COVID-19 pandemic, STOCHASTIC processes, RETAIL industry, EXTREME value theory |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Complementary Index |
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