Sparse-GEV: Sparse Latent Space Model for Multivariate Extreme Value Time Serie Modeling

Abstract

In many applications of time series models, such as climate analysis and social media analysis, we are often interested in extreme events, such as heatwave, wind gust, and burst of topics. These time series data usually exhibit a heavy-tailed distribution rather than a Gaussian distribution. This poses great challenges to existing approaches due to the significantly different assumptions on the data distributions and the lack of sufficient past data on extreme events. In this paper, we propose the Sparse-GEV model, a latent state model based on the theory of extreme value modeling to automatically learn sparse temporal dependence and make predictions. Our model is theoretically significant because it is among the first models to learn sparse temporal dependencies among multivariate extreme value time series. We demonstrate the superior performance of our algorithm to the state-of-art methods, including Granger causality, copula approach, and transfer entropy, on one synthetic dataset, one climate dataset and two Twitter datasets.