Changing Structures at Electricity Markets: Modelling spot prices using time-varying stable CARMA models

Abstract

Electricity markets are affected by rapidly changing structures, in particular due to the increasing share of renewable energies. Hence, the use of stationary time series models for modelling spot prices becomes more and more questionable. As a step towards the tractability of non-stationary time series we introduce in this paper a new class of stochastic processes which can be used in situations where the time series data at hand exhibit a non-stationary behaviour. These processes behave locally like classical stable processes although the parameters can vary over time. We illustrate the estimation of such processes using a straightforward maximum likelihood approach. Moreover, we show how the model can be applied to electricity spot prices. The approach of the paper can be transferred to other areas of applications and, therefore, should open the door to a new way of handling real-life phenomena with nonstationary behavior.