Langevin processes and time series: A look at data in power systems and paleoclimate data

Prof. Leonardo Rydin Gorjão presents his current research in the HDS-LEE / SSD Seminar Series: Langevin Processes and Time Series: A Look at Data in Power Systems and Paleoclimate Data.

Time series form one of the basis of data collection in science. An enormous collection of data-driven methods exist for time series analysis, many inspired by physics principles, either for one- or multi-dimensional time series. Among these, we find the likely simplest description of a ‘noisy’ time series: The Langevin process. It describes the motion of a particle influenced by a deterministic and a stochastic motion. Without the physics baggage, it describes a record or measurement with a ‘predictable’ continuous and an ‘unpredictable’ discontinuous term. We can usually reduce the description of a time series into a deterministic drift and a stochastic diffusion term, fundamentally solving an inverse problem of identifying ‘motion’ from data. In this presentation, we will revisit the Langevin equation – complicate it a bit – and look at what simple physics-inspired tools to uncover the drift, diffusion, and a few other properties, tell us about various types of data in power systems and paleoclimate data. Depending on the application, we will see that the stochastic nature of the data dictates a large portion of the important information of a stochastic process.