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A limit theorem for a class of stationary increments Levy moving average process with multiple singularities

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A limit theorem for a class of stationary increments Levy moving average process with multiple singularities. / Ljungdahl, Mathias Mørck; Podolskij, Mark.

In: Modern Stochastics: Theory and Applications, Vol. 5, No. 3, 09.2018, p. 297–316.

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Ljungdahl, Mathias Mørck ; Podolskij, Mark. / A limit theorem for a class of stationary increments Levy moving average process with multiple singularities. In: Modern Stochastics: Theory and Applications. 2018 ; Vol. 5, No. 3. pp. 297–316.

Bibtex

@article{390bf22ec8c3465dae89f64bab7fc2cb,
title = "A limit theorem for a class of stationary increments Levy moving average process with multiple singularities",
abstract = "In this paper we present some new limit theorems for power variations of stationary increment L{\'e}vy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt {\O}ksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models.",
keywords = "Fractional processes, High frequency data, Limit theorems, L{\'e}vy processes, Moving averages, Stable convergence, high frequency data, fractional processes, Levy processes, limit theorems, stable convergence, moving averages",
author = "Ljungdahl, {Mathias M{\o}rck} and Mark Podolskij",
year = "2018",
month = sep,
doi = "10.15559/18-VMSTA111",
language = "English",
volume = "5",
pages = "297–316",
journal = "Modern Stochastics: Theory and Applications",
issn = "2351-6046",
publisher = "ZTeX, Vilnius University & Taras Shevchenko National University of Kyiv",
number = "3",

}

RIS

TY - JOUR

T1 - A limit theorem for a class of stationary increments Levy moving average process with multiple singularities

AU - Ljungdahl, Mathias Mørck

AU - Podolskij, Mark

PY - 2018/9

Y1 - 2018/9

N2 - In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models.

AB - In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models.

KW - Fractional processes

KW - High frequency data

KW - Limit theorems

KW - Lévy processes

KW - Moving averages

KW - Stable convergence

KW - high frequency data

KW - fractional processes

KW - Levy processes

KW - limit theorems

KW - stable convergence

KW - moving averages

U2 - 10.15559/18-VMSTA111

DO - 10.15559/18-VMSTA111

M3 - Journal article

VL - 5

SP - 297

EP - 316

JO - Modern Stochastics: Theory and Applications

JF - Modern Stochastics: Theory and Applications

SN - 2351-6046

IS - 3

ER -