In the talk: “On the Forecastability of Time Series: a Fractal Perspective,” we will investigate a problem central to data forecasting: what characterizes time series data that is able to be accurately forecasted, especially within the context of modern neural network-based forecasting engines? To do this, we will first explore ideas of randomness, a theorem that feed forward neural networks are universal approximators for a certain class of functions, and we will explore functions from the unit interval into cantor lattices that neural network architectures in our experiments struggled to learn. We will then connect these results to ideas in Geometric-Measure Theory to inspire a fractal perspective in assessing the forecastibility of time series using the idea of Discrete S-Energy, a measure used to determine the fractal dimensionality of a point set.

We observe a stronger relationship between Discrete 1-Energy and forecast error on a class of synthetic time series than what exists between current industry standards and forecast error in experimentation. We then will explore experiments concerning the relationship between Discrete 1-Energy and forecast error on real life sales data from a large retailer.

This talk serves to motivate further investigation into fractal behavior within time series data sets and how it serves to affect our ability to forecast that data.