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.