Bayesian Time Series Forecasting with Change Point and Anomaly Detection

Anderson Y. Zhang, Miao Lu, Deguang Kong, Jimmy Yang

Abstract: Time series forecasting plays a crucial role in marketing, finance and many other quantitative fields. A large amount of methodologies has been developed on this topic, including ARIMA, Holt–Winters, etc. However, their performance is easily undermined by the existence of change points and anomaly points, two structures commonly observed in real data, but rarely considered in the aforementioned methods. In this paper, we propose a novel state space time series model, with the capability to capture the structure of change points and anomaly points, as well as trend and seasonality. To infer all the hidden variables, we develop a Bayesian framework, which is able to obtain distributions and forecasting intervals for time series forecasting, with provable theoretical properties. For implementation, an iterative algorithm with Markov chain Monte Carlo (MCMC), Kalman filter and Kalman smoothing is proposed. In both synthetic data and real data applications, our methodology yields a better performance in time series forecasting compared with existing methods, along with more accurate change point detection and anomaly detection.

TL;DR: We propose a novel state space time series model with the capability to capture the structure of change points and anomaly points, so that it has a better forecasting performance when there exist change points and anomalies in the time series.

Keywords: Time Series Forecasting, Change Point Detection, Anomaly Detection, State Space Model, Bayesian