Abstract: Technological advances have necessitated statistical methodologies for analyzing large-scale datastreams comprising multiple indefinitely time series. This article proposes a dynamic tracking and screening (DTS) framework for online learning and model updating. Utilizing the sequential nature of datastreams, a robust estimation approach is developed under a linear varying coefficient model framework. This accommodates unequally-spaced design points and updates coefficient estimates without storing historical data. A data-driven choice of an optimal smoothing parameter is proposed, alongside a new multiple testing procedure for the streaming environment. Statistical guarantees of the procedure are provided, along with simulation studies on its finite-sample performance. The methods are demonstrated through a mobile health example estimating when subjects' sleep and physical activities unusually influence their mood.

Key words and phrases: Consistency, kernel smoothing, multiple testing, varying coefficient.