# Nonlinear maximum likelihood estimation of electricity spot prices using recurrent neural networks

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## Abstract

Electricity spot prices are complex processes characterized by nonlinearity and extreme volatility. Previous work on nonlinear modeling of electricity spot prices has shown encouraging results, and we build on this area by proposing an Expectation Maximization algorithm for maximum likelihood estimation of recurrent neural networks utilizing the Kalman filter and smoother. This involves inference of both parameters and hyper-parameters of the model which takes into account the model uncertainty and noise in the data. The Expectation Maximization algorithm uses a forward filtering and backward smoothing (Expectation) step, followed by a hyper-parameter estimation (Maximization) step. The model is validated across two data sets of different power exchanges. It is found that after learning *a posteriori* hyper-parameters, the proposed algorithm outperforms the real-time recurrent learning and the extended Kalman Filtering algorithm for recurrent networks, as well as other contemporary models that have been previously applied to the modeling of electricity spot prices.

## Keywords

Electricity spot price Recurrent neural network Expectation maximization## References

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