Complex-Valued Time Series Based Solar Irradiance Forecast

TL;DR

This paper introduces a simple complex-valued autoregressive model for short-term solar irradiance forecasting, demonstrating comparable or better accuracy than classical models with minimal resources.

Contribution

It presents a novel complex-valued time series approach for solar irradiance prediction, expanding modeling possibilities with complex numbers in physics and related fields.

Findings

Root mean square error between 0.196 and 0.325

Comparable or better accuracy than Gaussian process and quantile regression

Model requires minimal resources and data

Abstract

This paper describes a new way to predict real time series using complex-valued elements. An example is given in the case of the short-term probabilistic global solar irradiance forecasts with measurement as real part and an estimate of the volatility as imaginary part. A simple complex autoregressive model is tested with data collected in Corsica island (France). Results show that, even if this approach is simple to set up and requires very little resource and data, both deterministic and probabilistic forecasts generated by this model are in agreement with experimental data (root mean square error ranging from 0.196 to 0.325 considering all studied horizons). In addition, it exhibits sometimes a better accuracy than classical models like Gaussian process, bootstrap methodology or even more sophisticated model like quantile regression. The number of models that it is possible to build by generating complex-valued time series is substantial. Indeed, by using exogenous or ordinal variables and computed quantities coupled with complex (or multi-complex) numbers, many studies and many fields of physics could benefit from this methodology and from the many models that result from it.