Limit theorems for stationary increments Lévy driven moving averages

Publikation: Working paperForskning


  • rp15_56

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In this paper we present some new limit theorems for power variation of k-th order increments of stationary increments Lévy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results, which (partially) have no counterpart in the theory of discrete moving averages. More specifically, we will show that the first order limit theorems and the mode of convergence strongly depend on the interplay between the given order of the increments, the considered power p, the Blumenthal-Getoor index of the driving pure jump Lévy process L and the behaviour of the kernel function g at 0. First order asymptotic theory essentially comprise three cases: stable convergence towards a certain infinitely divisible distribution, an ergodic type limit theorem and convergence in probability towards an integrated random process. We also prove the second order limit theorem connected to the ergodic type result. When the driving Lévy process L is a symmetric stable process we obtain two different limits: a central limit theorem and convergence in distribution towards a stable random variable.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider53
StatusUdgivet - 7 dec. 2015
SerietitelCREATES Research Papers


  • Power variation, limit theorems, moving averages, fractional processes, stable convergence, high frequency data

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