Causal Anomaly Detection in Multivariate Time Series with Information Entropy and Random Walk

Abstract

Significant causality change in multivariate time series is considered one of the primary anomalies in time series dynamics. However, observing causality changes with insufficient and irreproducible data, such as stock price and climate, is challenging. Therefore, we propose a method to detect substantial causal anomalies by generating causality and influence networks from multivariate time series. To form a causality network, each vertex represents a univariate time series. Each edge indicates the strength of the causality between each pair of time series using transfer entropy. With the causality network, we exploit the random walk approach to calculate the influence score between two vertices and create an influence network which reflects both direct and indirect causal influences. In the experiment, we show the validity of the proposed method by using a simple-structured synthetic time series network and analyzing information propagation. Also, we demonstrate how well the proposed networks reflect the status of multivariate time series by detecting anomalies in a real data set such as world stock indices and key performance indicators of an in-memory database system.