We discuss a deep learning based approach to model the complex dynamics of commodity prices observed in real markets. A regime-switching model is proposed to describe the time evolution of market prices. In this model, the base regime is described by a mean-reverting diffusion process and the second regime is driven by the predictions of a deep neural network trained on the market log-returns time series. A statistical technique, based on the method of simulated moments, is proposed to estimate the model on market data. We applied this methodology to energy commodity price time series with very different characteristics, namely the US wholesale electricity, natural gas and crude oil price daily time series. The obtained results show a good agreement with empirical data. In particular, the model seems to reproduce in a very interesting way the first four central moments of the empirical distributions of log-returns as well as the shape of the observed price time series.

A model is proposed to investigate the effects of power generation source diversification and CO₂ emission control in the presence of dispatchable fossil fuel sources and non-dispatchable carbon-free renewables. In a stochastic environment in which three random factors are considered, namely fossil fuels (gas and coal) and CO₂ prices, we discuss a planning methodology for power system portfolio selection that integrates the non-dispatchable renewables available in a given energy system and optimally combines cost, risk and CO₂ emissions. By combining the deep neural network probabilistic forecasting of fossil fuel path prices with a geometric Brownian motion model for describing the CO₂ price dynamics, we simulate a wide range of plausible market scenarios. Results show that under CO₂ price volatility, optimal portfolios shift toward cleaner energy sources, even in the absence of explicit emission targets, highlighting the implicit regulatory power of volatility. The results suggest that incorporating CO₂ price volatility through market mechanisms can serve as an effective policy tool for driving decarbonization. Our model offers a flexible and reproducible approach to support policy design in energy planning under uncertainty.

Accurate estimation of the mean-reversion speed $\alpha$ in the AR(1) process $X_{t+1}=(1-\alpha )X_t+{\epsilon }_t$ is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by embedding $\alpha$ within distributional assumptions, so that different model choices yield different $\widehat{\alpha }$ values from the same series without a principled criterion to adjudicate. We propose a distribution-free neural estimator based on a Temporal Convolutional Network (TCN) trained on synthetic AR(1) series with Sinh-ArcSinh (SAS) innovations. Distribution-free here means that no parametric family is assumed for the innovation distribution at inference time: the estimator imposes no distributional hypothesis when processing a new series. The SAS family serves as a training vehicle—not a model for the real data—chosen for its ability to span a broad range of tail weights and asymmetry profiles. The theoretical foundation is spectral invariance: the Yule–Walker equations establish that the autocorrelation structure ${\rho }_k={(1-\alpha )}^k$ depends on $\alpha$ alone, provided innovations are uncorrelated across lags—a condition satisfied not only by i.i.d. innovations but also by conditionally heteroscedastic processes such as GARCH. The TCN therefore generalises to volatility-clustering environments without modification, learning to extract $\alpha$ from temporal dependence alone, independently of the marginal innovation distribution and of the temporal variance structure. On held-out test series the estimator outperforms all classical competitors, with the advantage growing monotonically with non-Gaussianity. A robustness analysis on three out-of-distribution innovation families and on AR(1)-GARCH(1,1) processes empirically validates the spectral invariance guarantee across both marginal and temporal variance structure, including near-integrated GARCH processes where innovation kurtosis far exceeds the training range. The distribution-free $\widehat{\alpha }$ enables a two-stage pipeline in which $\alpha$ and the innovation distribution are characterised independently—a decoupling structurally impossible in classical likelihood-based approaches. Once trained, the TCN acts as a universal mean-reversion estimator applicable to any price series without re-fitting. Applied to four energy markets—Italian natural gas (PSV price), Italian electricity (PUN price), US Henry Hub, and US PJM West Hub—spanning log-return kurtosis from near-Gaussian to strongly heavy-tailed, the TCN yields robust, distribution-free estimates of mean-reversion speed.

In the spirit of Occam’s razor, we propose a parsimoniuos regime-switching model for describing the complex dynamics of electricity and natural gas prices observed in real markets. The model was built using a machine learning-based methodology, namely a cluster analysis to investigate the properties of the stable dynamics and a deep neural network appropriately trained on market data to drive transitions between different regimes. The main purposes of this study are twofold: (1) to build the simplest model capable of incorporating the main stylized facts of electricity and natural gas prices, including dynamic correlation; (2) to define an appropriate calibration procedure on market data. We applied this methodology to the Italian energy market. The results obtained show remarkable agreement with the empirical data, satisfactorily reproducing the first four moments of the empirical distributions of log-returns.