Generalized Mixture Model for Extreme Events Forecasting in Time Series Data

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.