Generalized Mixture Model for Extreme Events Forecasting in Time Series
  Data
Jincheng Wang Yue Gao
Time Series Forecasting (TSF) is a widely researched topic with broad
applications in weather forecasting, traffic control, and stock price
prediction. Extreme values in time series often significantly impact human and
natural systems, but predicting them is challenging due to their rare
occurrence. Statistical methods based on Extreme Value Theory (EVT) provide a
systematic approach to modeling the distribution of extremes, particularly the
Generalized Pareto (GP) distribution for modeling the distribution of
exceedances beyond a threshold. To overcome the subpar performance of deep
learning in dealing with heavy-tailed data, we propose a novel framework to
enhance the focus on extreme events. Specifically, we propose a Deep Extreme
Mixture Model with Autoencoder (DEMMA) for time series prediction. The model
comprises two main modules: 1) a generalized mixture distribution based on the
Hurdle model and a reparameterized GP distribution form independent of the
extreme threshold, 2) an Autoencoder-based LSTM feature extractor and a
quantile prediction module with a temporal attention mechanism. We demonstrate
the effectiveness of our approach on multiple real-world rainfall datasets.