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On limit theory for functionals of stationary increments Lévy driven moving averages

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On limit theory for functionals of stationary increments Lévy driven moving averages. / Basse-O'Connor, Andreas; Heinrich, Claudio; Podolskij, Mark.

In: Electronic Journal of Probability, Vol. 24, 79, 09.2019.

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@article{80dc08d904ed42aa9d7bad8b0aac8674,
title = "On limit theory for functionals of stationary increments L{\'e}vy driven moving averages",
abstract = "In this paper we present new limit theorems for variational functionals of stationary increments Levy driven moving averages in the high frequency setting. More specifically, we will show the {"}law of large numbers'' and a {"}central limit theorem'', which heavily rely on the kernel, the driving Levy process and the properties of the functional under consideration. The first order limit theory consists of three different cases. For one of the appearing limits, which we refer to as the ergodic type limit, we prove the associated weak limit theory, which again consists of three different cases. Our work is related to a recent work on power variation functionals of stationary increments Levy driven moving averages. However, the asymptotic theory of the present paper is more complex. In particular, the weak limit theorems are derived for an arbitrary Appell rank of the involved functional.",
author = "Andreas Basse-O'Connor and Claudio Heinrich and Mark Podolskij",
year = "2019",
month = sep,
doi = "10.1214/19-EJP336",
language = "English",
volume = "24",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - On limit theory for functionals of stationary increments Lévy driven moving averages

AU - Basse-O'Connor, Andreas

AU - Heinrich, Claudio

AU - Podolskij, Mark

PY - 2019/9

Y1 - 2019/9

N2 - In this paper we present new limit theorems for variational functionals of stationary increments Levy driven moving averages in the high frequency setting. More specifically, we will show the "law of large numbers'' and a "central limit theorem'', which heavily rely on the kernel, the driving Levy process and the properties of the functional under consideration. The first order limit theory consists of three different cases. For one of the appearing limits, which we refer to as the ergodic type limit, we prove the associated weak limit theory, which again consists of three different cases. Our work is related to a recent work on power variation functionals of stationary increments Levy driven moving averages. However, the asymptotic theory of the present paper is more complex. In particular, the weak limit theorems are derived for an arbitrary Appell rank of the involved functional.

AB - In this paper we present new limit theorems for variational functionals of stationary increments Levy driven moving averages in the high frequency setting. More specifically, we will show the "law of large numbers'' and a "central limit theorem'', which heavily rely on the kernel, the driving Levy process and the properties of the functional under consideration. The first order limit theory consists of three different cases. For one of the appearing limits, which we refer to as the ergodic type limit, we prove the associated weak limit theory, which again consists of three different cases. Our work is related to a recent work on power variation functionals of stationary increments Levy driven moving averages. However, the asymptotic theory of the present paper is more complex. In particular, the weak limit theorems are derived for an arbitrary Appell rank of the involved functional.

U2 - 10.1214/19-EJP336

DO - 10.1214/19-EJP336

M3 - Journal article

VL - 24

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

M1 - 79

ER -