Learning volatility of discrete time series using prediction with expert advice

Abstract

In this paper the method of prediction with expert advice is applied for learning volatility of discrete time series. We construct arbitrage strategies (or experts) which suffer gain when "micro" and "macro" volatilities of a time series differ. For merging different expert strategies in a strategy of the learner, we use some modification of Kalai and Vempala algorithm of following the perturbed leader where weights depend on current gains of the experts. We consider the case when experts one-step gains can be unbounded. New notion of a volume of a game vt is introduced. We show that our algorithm has optimal performance in the case when the one-step increments Δvt = vt - vt-1 of the volume satisfy Δvt = o(vt) as t → ∞. © Springer-Verlag 2009.