  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.
