Spliced Binned-Pareto Distribution for Robust Modeling of Heavy-tailed Time Series

• URL: http://arxiv.org/abs/2106.10952v1
• Date: Mon, 21 Jun 2021 09:48:03 GMT
• Title: Spliced Binned-Pareto Distribution for Robust Modeling of Heavy-tailed Time Series
• Authors: Elena Ehrlich, Laurent Callot, Fran\c{c}ois-Xavier Aubet
• Abstract summary: We propose a novel method to robustly and accurately model time series with heavy-tailed noise. Our method allows the capture of time dependencies in the higher order moments of the distribution. We compare the robustness and the accuracy of our method to other state of the art methods on Twitter mentions count time series.
• Score: 1.0312968200748118
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the performance of classical forecasting models; in particular, accurately modeling a distribution over extreme events is crucial to performing accurate time series anomaly detection. We propose a Spliced Binned-Pareto distribution which is both robust to extreme observations and allows accurate modeling of the full distribution. Our method allows the capture of time dependencies in the higher order moments of the distribution such as the tail heaviness. We compare the robustness and the accuracy of the tail estimation of our method to other state of the art methods on Twitter mentions count time series.

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