Defining Single Asset Price Momentum in terms of a Stochastic Process

Abstract

This paper looks at various definitions of momentum then investigates a particular definition of momentum via a statistical model where the asset price is assumed to follow a log Ornstein–Uhlenbeck process. Momentum is a term that is widely used to describe price behaviour but is not clearly defined in terms of statistical models. The results we derive show that asset price momentum is determined by price autocorrelation and that positive momentum, as commonly understood, would require explosive behaviour in log prices.