Fast Methods for Statistical Arbitrage

Abstract

In many time series applications, the data set under study is a vast stream of continuously updated data. Often those data arrive in bursts. Many examples are found in finance, telecommunications, physics, biology, astronomy, among others. The main motivation of our project is to infer linear relationships among multiple financial variables, yielding expressions of the form 4∗DJI−35∗SNP500=2.4∗NASDAQ$4*\mathrm{DJI} - 35*\mathrm{SNP}500 = 2.4*\mathrm{NASDAQ}$. We use such relationships to back-test a simple trading strategy. For the most part we based our analyses on FOREX data but we also experimented with non-financial datasets. Finally, we provide software capable of being used in a variety of generalized machine learning and streaming applications in many environments. The framework we developed is named StatLearn and is based on two fundamental blocks: SketchStream to filter for relevant time series (a reimplementation of StatStream) and LearnStream to make predictions. Thus, we provide machine learning algorithms in an on-line context.