Hierarchical Vector Mixtures for Electricity Day-Ahead Market Prices Scenario Generation

In this paper a class of fully probabilistic time series models based on Gaussian Vector Mixtures (VMs), i.e., Gaussian multivariate mixtures, is proposed to model electricity Day Ahead Market (DAM) hourly prices and to generate related future scenarios. These models intrinsically allow for organizing data in clusters, their parameters having a simple and clear interpretation in terms of market phenomenology, like spikes and night/day seasonality. Differently from current deep learning models, VMs and the other members of the class discussed in the paper, often seen as just `old style’ machine learning in the machine learning community, are shown to be directly interpretable as a subset of the regime switching autoregressions still currently largely used in the econometric community. The paper can be thought as divided in two parts. In the first part, VMs are estimated and used to model daily vector sequences of 24 prices, thus assessing their scenario generation capability. In this part it is shown that VMs can hierarchically cluster data, can preserve and encode very well intraday dynamic structure like autocorrelation up to 24 lags, but also that they cannot handle interday structure. In the second part, these mixtures are dynamically extended to incorporate features typical of hidden Markov models, thus becoming Vector Hidden Markov Mixtures (VHMMs). VHMMs are shown to be able to model both intraday and interday phenomenology, hence able to include autocorrelation beyond 24 lags. They are also shown to possess enough internal structure to exploit and carry forward hierarchical clustering in their dynamics, their small number of parameters still preserving a simple and clear interpretation in terms of market phenomenology and in terms of standard econometrics. All these properties are thus also available to their regime switching counterparts. In practice, these very simple models are able to learn latent price regimes from historical data in an unsupervised fashion, enabling the generation of realistic market scenarios and also probabilistic forecasts, while maintaining straightforward econometrics-like explanability.