Statistical properties of signal entropy for use in detecting changes in time series data

Detecting changes in an underlying time series model for a system is an important task in many different fields, including econometrics, geophysics and process control. Specifically, in process control, detecting model changes is often the first step for fault detection, plant‐model mismatch assessment and data quality assessment for system identification. Signal entropy, which basically measures the amount of disorder in a given signal, can, not only segment a time series, but can also determine which regions have similar underlying models. Thus, the changes between the input and output signals can be used to determine when model is no longer an accurate representation of the system by comparing the current differential entropy against the historical differential entropy. This paper presents the statistical properties of signal entropy for discrete time systems. An example of the general results is provided by determining the entropy characteristics for first‐order systems driven by white noise. As well, a change detection index is proposed to assess changes in the time series model, which is tested on an experimental system. Copyright © 2013 John Wiley & Sons, Ltd.