Year: 2021
Type: article
Abstract: This paper presents new limit theorems for power variations of fractional type symmetric infinitely divisible random fields. More specifically, the random field X=(X(t))t∈[0,1]d is defined as an integral of a kernel function g with respect to a symmetric infinitely divisible random measure L and is observed on a grid with mesh size n−1. As n→∞, the first order limits are obtained for power variation statistics constructed from rectangular increments of X. The present work is mostly related to [8, 9], who studied a similar problem in the case d=1. We will see, however, that the asymptotic theory in the random field setting is much richer compared to [8, 9] as it contains new limits, which depend on the precise structure of the kernel g. We will give some important examples including the Lévy moving average field, the well-balanced symmetric linear fractional β-stable sheet, and the moving average fractional β-stable field, and discuss potential consequences for statistical inference.
DOI: 10.1214/21-ejp617
Institutions: Aarhus University, University of Luxembourg
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $675
Funder: Villum Fonden
OpenAlex ID: W3046933424