Before revision: Regression analysis aims to use observational data from multiple observations to develop a functional relationship relating explanatory variables to response variables, which is important for much of modern statistics, and econometrics, and also the field of machine learning. In this paper, we consider the special case where the explanatory variable is a stream of information, and the  response is also potentially a stream.
After revision: We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the response is also potentially a stream.