2016/04/08 by Andreas Basse-O’Connor, Claudio Heinrich, Basse-O'Connor, Andreas +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1604.02307
openalex publication_date 2016/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we present some limit theorems for power variation of Lévy semi-stationary processes in the setting of infill asymptotics. Lévy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving average type processes with a multiplicative random component, which is usually referred to as volatility or intermittency. From the mathematical point of view this work extends the asymptotic theory investigated in [14], where the authors derived the limit theory for kth order increments of stationary increments Lévy driven moving averages. The asymptotic results turn out to heavily depend on the interplay between the given order of the increments, the considered power p>0, the Blumenthal--Getoor index β∈ (0,2) of the driving pure jump Lévy process L and the behaviour of the kernel function g at 0 determined by the power α. In this paper we will study the first order asymptotic theory for Lévy semi-stationary processes with a random volatility/intermittency component and present some statistical applications of the probabilistic results.