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NAERINGSPH-Nærings-phd

Quantum Harmonic Analysis and its application to Time Series Forecasting

Alternative title: Quantum Harmonic Analysis and its application to Time Series Forecasting

Awarded: NOK 1.8 mill.

Project Manager:

Project Number:

332875

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Project Period:

2022 - 2024

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This research project aims to improve forecasting techniques for continuous time series, with a view to energy market forecasting to improve energy production optimisation. Recent developments in Quantum Harmonic Analysis, an intersection of progress in mathematical physics and time-frequency analysis, have given rise to new ways of considering the structure of data sets. Tools from Quantum Information Theory provide insights into effective dimensionality of data, informing how one might approach issues in time series forecasting. In the continuous setting of energy demand over each day, one can consider the data set as a time series of curves, with each curve corresponding to each day. Since the space of such curves is infinitely dimensional, the practicality of this approach is limited by an understanding of how to reduce the problem to a finite dimensional setting. In this sense Quantum Harmonic Analysis provides a framework for interpreting the information contained within the data. The project will initially develop the theoretical underpinnings of the approach of Quantum Harmonic Analysis and Information Theory, and later on consider the application of developments to energy market forecasting, and how such forecasts can be incorporated into energy production optimisation for operators.

This project aims to explore new ways of exploring high dimensional data and using this to forecast functional time series, i.e. where data is given as a time-indexed sequence of functions. A common problem in this domain is the effective reduction of an infinite-dimensional object to a finite-dimensional one. We aim to explore recent developments in quantum harmonic analysis to be able to place estimates on errors involved in dimensionality reduction in order to be able to model problems on a more reasonably sized data space. In particular, using these methods we aim to investigate how infinitely dimensional dynamic functional principal components can be reduced to a meaningful finite subset in order to apply them productively to time series forecasting. This work will then be applied to industrial problems being faced today, especially within the space of energy market operations where market participants are in need of accurate price and demand forecasts to make optimal trading decisions. The project will implement these new techniques to problems in energy market forecasting, and compare the results with current state of the art methods.

Funding scheme:

NAERINGSPH-Nærings-phd