Theory and Algorithms for Forecasting Non-Stationary Time Series

Time series appear in a variety of key real-world applications such as signal processing, including audio and video processing; the analysis of natural phenomena such as local weather, global temperature, and earthquakes; the study of economic variables such as stock values, sales amounts, energy demand; and many other areas. But, while time series forecasting is critical for many applications, it has received little attention in the ML community in recent years, probably due to a lack of familiarity with time series and the fact that standard independent and identically distributed learning concepts and tools are not readily applicable in that scenario.

This tutorial precisely addresses these and many other related questions. It provides theoretical and algorithmic tools for research related to time series and for designing new solutions. We first present a concise introduction to time series, including basic concepts, common challenges and standard models. Next, we discuss important statistical learning tools and results developed in recent years and show how they are useful for deriving guarantees and designing algorithms both in stationary and non-stationary scenarios. Finally, we show how the online learning framework can be leveraged to derive algorithms that tackle important and notoriously difficult problems including model selection and ensemble methods.