Modelling the working week for multi-step forecasting using Gaussian process regression

Abstract

In time-series forecasting, regression is a popular method, with Gaussian Process Regression widely held to be the state of the art. The versatility of Gaussian Processes has led to them being used in many varied application domains. However, though many real-world applications involve data which follows a working-week structure, where weekends exhibit substantially different behaviour to weekdays, methods for explicit modelling of working-week effects in Gaussian Process Regression models have not been proposed. Not explicitly modelling the working week fails to incorporate a significant source of information which can be invaluable in forecasting scenarios. In this work we provide novel kernel-combination methods to explicitly model working-week effects in time-series data for more accurate predictions using Gaussian Process Regression. Further, we demonstrate that prediction accuracy can be improved by constraining the non-convex optimisation process of finding optimal hyperparameter values. We validate the effectiveness of our methods by performing multistep prediction on two real-world publicly available time-series datasets - one relating to electricity Smart Meter data of the University of Melbourne, and the other relating to the counts of pedestrians in the City of Melbourne.