Data-driven model discovery for coupled time series

Model discovery techniques can help discover plausible candidate models from data and can aid theory-building in areas of cognitive science where empirical work has not yet led to formal specification. In this project we introduce a data-driven framework for discovery of parsimonious stochastic differential equation models from time series data in two or more dimensions. We discuss the theoretical foundation of the framework from stochastic calculus and illustrate the application to coupled time series. We first demonstrate the general approach through numerical examples. Then, we evaluate the viability of an extended approach in which we include exogenous predictors in both the deterministic and the stochastic components of the discovered model. Finally, we will discuss the development and use of inferential statistics within this framework. We illustrate the framework with an application in which we explore the relationship dynamics between dimensions of core affect from a daily life study.