Nicolás Coloma Carphio, Department of Computer Science, University of Colorado Boulder

Prediction and Inference for high frequency spatiotemporal data

In this talk we will address problems posed by two challenging high-frequency space-time datasets.

As the power grid transitions to a renewable future, integrating weather-driven energy sources like solar power presents challenges due to their variability, non-Gaussianity, and intermittency. Realistic high-resolution data are essential for grid planning but are often unavailable. Given sparse spatial samples, we introduce a framework for spatiotemporal prediction in a functional data analysis framework when data exhibit nonstationary phase misalignment.  The approach is illustrated on a high frequency irradiance dataset and compared with existing methods.

The second problem addressed is in the realm of financial modeling. Many time series exhibit sudden jumps that classical stochastic models struggle to capture. Lévy processes provide a natural framework for such behavior, but parameter estimation is challenging when the likelihood is intractable. We explore neural Bayes estimation as a promising alternative, applying it to general Lévy processes and test on a difficult case study involving deep variance gamma processes, showcasing their estimation and potential applications.

 Passcode for this talk is math-geo