Thiele-CREATES Seminar: Mikko Pakkanen, Aarhus University and CREATES

Abstract:

Typically, power variations of a Brownian semistationary (BSS) process converge in probability only if they are scaled appropriately, and such scaling depends on a unknown parameter. We introduce the concept of relative power variation, which is a feasible statistic that converges (without any additional scaling) to a relative integrated volatility functional. This consistency property is rather robust; in fact, it is valid for both BSS processes and Itô semimartingales. We also establish a stable functional central limit theorem for relative power variations in these settings. The talk is based on joint work with Ole E. Barndorff-Nielsen and Jürgen Schmiegel.