Mixture Factorized Ornstein-Uhlenbeck Processes for Time-Series Forecasting

Forecasting the future observations of time-series data can be performed by modeling the trend and fluctuations from the observed data. Many classical time-series analysis models like Autoregressive model (AR) and its variants have been developed to achieve such forecasting ability. While they are often based on the white noise assumption to model the data fluctuations, a more general Brownian motion has been adopted that results in Ornstein-Uhlenbeck (OU) process. The OU process has gained huge successes in predicting the future observations over many genres of time series, however, it is still limited in modeling simple diffusion dynamics driven by a single persistent factor that never evolves over time. However, in many real problems, a mixture of hidden factors are usually present, and when and how frequently they appear or disappear are unknown ahead of time. This imposes a challenge that inspires us to develop a Mixture Factorized OU process (MFOUP) to model evolving factors. The new model is able to capture the changing states of multiple mixed hidden factors, from which we can infer their roles in driving the movements of time series. We conduct experiments on three forecasting problems, covering sensor and market data streams. The results show its competitive performance on predicting future observations and capturing evolution patterns of hidden factors as compared with the other algorithms.