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Abstract:
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A conventional approach to the extraction of latent components in a time series is to first model extreme values and outliers (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 pertaining to this identification -- as well as the removal of extremes -- goes unmeasured. Alternatively, each type of 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.
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