Rolling Gaussian Process Regression with Application to Regime Shifts

Gaussian Process Regression (GPR) can be applied to the problem of estimating a spatially-varying field on a regular grid, based on noisy observations made at irregular positions. In cases where the field has a weak time dependence, one may desire to estimate the present-time value of the field using a time window of data that rolls forward as new data become available, leading to a sequence of solution updates. We introduce “rolling GPR” (or moving window GPR) and present a procedure for implementing that is more computationally efficient than solving the full GPR problem at each update. Furthermore, regime shifts (sudden large changes in the field) can be detected by monitoring the change in posterior covariance of the predicted data during the updates, and their detrimental effect is mitigated by shortening the time window as the variance rises, and then decreasing it as it falls (but within prior bounds). A set of numerical experiments is provided that demonstrates the viability of the procedure.