Statistical monitoring of spatio-temporal processes

A04 develops methodology for online monitoring in spatio-temporal models and timely detection of structural alterations. It develops robust procedures, considers tail behavior in form of, e.g., extreme quantiles and investigates high-dimensional scenarios with many variables. The long-term goal is the development of robust monitoring tools for various classes of nonlinear spatio-temporal processes and for high-dimensional mixed-frequency data.

We develop novel methods for online monitoring of the validity and the stability of complex spatio-temporal models (STMs) with a particular focus on applications in energy and transport. Online monitoring is conducted using statistical decision rules (so-called control charts). These charts evaluate at every new time point whether the model is still adequate or not by comparing a control statistic to critical limits, which need to be chosen such that certain performance criteria are met concerning both the frequency of false alarms in the former and the detection delay in the latter case. By designing monitoring tools for STMs we confront the challenges of finding appropriate sparse statistical representations for these complex modeling scenarios and deriving their statistical properties. We consider STMs in various settings where we (a) incorporate autoregressive features for both space (e.g., the network structure) and time, (b) develop procedures that are robust with respect to restrictive distributional assumptions, (c) consider quantiles and the tail behaviour of spatial data, and (d) treat multivariate and high-dimensional settings and apply appropriate dimension reduction techniques for making STMs empirically tractable. Our methods will enable a timely detection of changes in STM parameters and more generally of model deficiencies. This is of essential importance for using such models in applications, in particular for adequate prediction.