  Detecting changes in data streams is a vital task in many applications. There
is increasing interest in changepoint detection in the online setting, to
enable real-time monitoring and support prompt responses and informed
decision-making. Many approaches assume stationary sequences before
encountering an abrupt change in the mean or variance. Notably less attention
has focused on the challenging case where the monitored sequences exhibit
trend, periodicity and seasonality. Dynamic mode decomposition is a data-driven
dimensionality reduction technique that extracts the essential components of a
dynamical system. We propose a changepoint detection method that leverages this
technique to sequentially model the dynamics of a moving window of data and
produce a low-rank reconstruction. A change is identified when there is a
significant difference between this reconstruction and the observed data, and
we provide theoretical justification for this approach. Extensive simulations
demonstrate that our approach has superior detection performance compared to
other methods for detecting small changes in mean, variance, periodicity, and
second-order structure, among others, in data that exhibits seasonality.
Results on real-world datasets also show excellent performance compared to
contemporary approaches.
