We propose a machine learning-based methodology which makes use of ensemble methods with the aims (i) of treating missing data in time series with irregular observation times and detecting anomalies in the observed time behavior; (ii) of defining suitable models of the system dynamics. We applied this methodology to US wholesale electricity price time series that are characterized by missing data, high and stochastic volatility, jumps and pronounced spikes. For missing data, we provide a repair approach based on the missForest algorithm, an imputation algorithm which is completely agnostic about the data distribution. To identify anomalies, i.e., turbulent movements of power prices in which jumps and spikes are observed, we took into account the no-gap reconstructed electricity price time series, and then we detected anomalous regions using the isolation forest algorithm, an anomaly detection method that isolates anomalies instead of profiling normal data points as in the most common techniques. After removing anomalies, the additional gaps will be newly filled by the missForest imputation algorithm. In this way, a complete and clean time series describing the stable dynamics of power prices can be obtained. The decoupling between the stable motion and the turbulent motion allows us to define suitable jump-diffusion models of power prices and to provide an estimation procedure that uses the full information contained in both the stable and the turbulent dynamics.

The paper uses text mining and semantic algorithms to tag innovative firms and offer an alternative perspective to classify industrial activities. Instead of referring to firms’ standard industrial classification codes, we gather information from companies’ websites and corporate purposes, extract keywords and generate tags concerning firms’ activities, specializations, and competences. Evidence is interesting because allows us to understand ‘what firms do’ in a more penetrating and updated way than referring to standard industrial classification codes. Moreover, through matching firms’ keywords, we can explore the degree of closeness between the firms under observation, a measure by which researchers can derive industrial proximity. The analysis can provide policymakers with a detailed and comprehensive picture of the innovative trajectories underlying the industrial structure in a geographic area.

A fully unsupervised graph-based superframework is proposed to handle the EM initialization problem for estimating mixture models on financial time series. Using a complex network approach that links time series and graphs, the graph-structured information derived from the observed data is exploited to produce a meaningful starting point for the EM algorithm. It is shown that structural information derived by complex graphs can definitely capture time series behavior and nonlinear relationships between different observations. The proposed methodology is employed to estimate Gaussian mixture models on US wholesale electricity market prices using two different configurations of the superframework. The obtained results show that the proposed methodology performs better than conventional initialization methods, such as K-means based techniques. The improvements are significant on the overall representation of the empirical distribution of log-returns and, in particular, on the first four moments. Moreover, this approach has a high degree of generalization and flexibility, exploiting graph manipulation and employing functional operating blocks, which can be adapted to very different empirical situations.

A novel methodology is proposed for jointly modeling the price dynamics of natural gas and electricity by integrating graph‐based Machine Learning and optimal transport theory. The framework combines visibility graph embeddings with the Wasserstein barycenter to uncover latent structures and asymmetric dependencies between the two interconnected energy markets. Log‐return time series are first transformed into visibility graphs and then embedded into high‐dimensional vector spaces, where complex temporal and structural patterns become more discernible. In the embedding space, an information‐driven Wasserstein barycenter is computed by optimizing the barycenter weights via Shannon entropy maximization. This procedure reveals an asymmetric balance between the two markets, with natural gas exerting a structurally dominant influence. To characterize the joint stochastic dynamics, a Gaussian Mixture Model is fitted to the thus determined unbalanced Wasserstein barycenter using maximum likelihood estimation via the Expectation–Maximization algorithm. An additional Gaussian component is introduced for each commodity to capture market‐specific behavior. The resulting model can be calibrated to match the first four moments of the empirical log‐return distributions and their observed correlation. Applied to Italian market data from 2019 to 2023, a period marked by extreme volatility and systemic shocks, the methodology accurately reproduces both common dynamics and idiosyncratic deviations. The analysis reveals that the entropy‐optimal barycentric weights are for natural gas and for electricity, highlighting a dominant role of the natural gas market in the joint representation. Compared with a comprehensive benchmark of GARCH‐type models, the proposed framework exhibits markedly superior empirical performance. The approach provides a robust, interpretable, and adaptable tool for risk analysis, derivative pricing, and the study of structural interactions across energy markets.