Quantile Fourier regressions for decision making under uncertainty

TL;DR

This paper introduces a novel approach for modeling time-inhomogeneous Markov decision processes with periodic behaviors, enabling better decision-making under uncertainty in natural phenomena like hydropower and wind power.

Contribution

It presents a new technique for constructing cyclostationary Markov processes that incorporate periodic variations in values and dependence structures.

Findings

Effective modeling of periodic natural phenomena.

Improved decision-making in hydropower scheduling.

Enhanced integration of offshore wind power.

Abstract

Weconsider Markov decision processes arising from a Markov model of an underlying natural phenomenon. Such phenomena are usually periodic (e.g. annual) in time, and so the Markov processes modelling them must be time-inhomogeneous, with cyclostationary rather than stationary behaviour. We describe a technique for constructing such processes that allows for periodic variations both in the values taken by the process and in the serial dependence structure. We include two illustrative numerical examples: a hydropower scheduling problem and a model of offshore wind power integration.