Model Agnostic Methods for Multivariate Time Series with Arbitrary Dependence

Nonlinear functional dependence in temporal data can be challenging to characterize. Linear methods often oversimplify the structure of data, and imposition of a rigid framework can be be limiting. A model-based method that is "close enough" usually works well, but specification of this functional form can be difficult, especially in dependent, multivariate data and when lacking a deep scientific understanding of the process. Representation learning methods, employing artificial neural networks, provide a model agnostic approach to capture even the most complicated and intricate interactions between covariates. These methods, if applied cautiously and when model recovery is not the main goal, can alleviate the burden of model specification and the difficulties that arise from model misspecification. They are applied to single and multiple change point detection, the adaptation of Granger causality to nonlinear functional dependence, and discussions of future research include strategic workarounds for the loss of covariate-specific and relational information.