A high-dimensional VARX model to simulate monthly renewable energy supply

Abstract

This paper proposes a novel framework for forecasting and simulating renewable energy on a long-term horizon. In this regard, it is presented a monthly multivariate stochastic model for wind and hydro inflow as well as an efficient estimation method for high-dimensional data. Firstly, in order to model the inherent uncertainty of renewable energy supplies, this work proposes a high-dimensional VARX with periodic variance. Secondly, an estimation procedure is suggested based on the maximum likelihood criterion with endogenous variable selection. Due to the presence of multicollinearity and high-dimensionality, the estimation procedure proposed in this work has two main features: (i) a fixed-point algorithm to pursue the maximum likelihood estimators under periodic heteroskedasticity (ii) obtain a sparse solution by means of ℓ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -regularization. Simulations and forecasting results for a real case study involving fifty Brazilian renewable power plants are presented.