Controlling Nonstationarity in Statistical Arbitrage Using a Portfolio of Cointegration Models

Abstract

We present an analysis of time-series modelling which allows for the possibility of an “unmodelled” component which is present in the underlying generating process, but is not captured in a particular “model” of the time-series. Within this framework, “nonstationarity” is a relative, rather than an absolute, property, which is conditional on a given data representation, model and/or set of parameters. We apply this perspective to the problem of trading statistical arbitrage models which are based on the econometric notion of weak cointegration between asset prices. We show how a modelling framework which supports multiple models may reduce the out-of-sample performance degradation which is caused by non-stationarities in the relative price dynamics of the set of target assets. A necessary condition is shown to be that the unmodelled components of the individual models must be less than perfectly correlated, thus motivating the use of a population-based algorithm which jointly optimises a portfolio of decorrelated models. We describe an application of this methodology to trading statistical arbitrage between equity index futures and present empirical results, before concluding with a brief discussion of the issues raised and an outline of ongoing developments.