Limit theorems for stationary increments Lévy driven moving averages

Andreas Basse-O'Connor (), Raphaël Lachièze-Rey () and Mark Podolskij ()
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Andreas Basse-O'Connor: Department of Mathematics, Postal: Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark
Raphaël Lachièze-Rey: Heidelberg University - Department of Mathematics, Postal: Heidelberg University, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
Mark Podolskij: Department of Mathematics and CREATES, Postal: Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: 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.

Keywords: Power variation; limit theorems; moving averages; fractional processes; stable convergence; high frequency data (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 53
Date: 2015-12-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (3)

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