Data-Driven Methods for Time Series Forecasting, Classification, and Uncertainty Quantification

Abstract

The increased availability of time series data has led to a burgeoning interest in data-driven modeling and time series analysis. The ability to model temporal data can not only enable us to discover patterns inherent in a set of collected measurements, but also predict future trends. However, collected temporal measurements are oftentimes artifacted with noise, making it difficult to discern the actual signal. This presence of noise can greatly bias models, resulting in inaccurate forecasts with high uncertainty. In this thesis,I demonstrate how data-driven methods can be applied to a wide array of artifacted data while circumventing noise-induced bias.I first show the application of various data-driven methods and signal processing techniques on labeled time series data. Specifically, I apply supervised machine learning and signal processing techniques on corrupted electrocardiograms (ECGs) in order to classify pulse status in patients undergoing cardiac arrest. I then introduce a data-driven method that leverages statistical bagging and optimized Dynamic Mode Decomposition (optDMD) in order to produce accurate long-term forecasting and spatial and temporal uncertainty quantification for unlabeled, non-stationary time series. I then highlight the robustness of this method by applying it to corrupted flu transmission data in order to predict future flu trends as well as gain insight into temporal cycles of modes.