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Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages

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Standard

Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages. / Nielsen, Mikkel Slot; Pedersen, Jan.

I: ESAIM: Probability & Statistics, Bind 23, 2019, s. 803-822.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Harvard

Nielsen, MS & Pedersen, J 2019, 'Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages', ESAIM: Probability & Statistics, bind 23, s. 803-822. https://doi.org/10.1051/ps/2019008

APA

Nielsen, M. S., & Pedersen, J. (2019). Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages. ESAIM: Probability & Statistics, 23, 803-822. https://doi.org/10.1051/ps/2019008

CBE

Nielsen MS, Pedersen J. 2019. Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages. ESAIM: Probability & Statistics. 23:803-822. https://doi.org/10.1051/ps/2019008

MLA

Nielsen, Mikkel Slot og Jan Pedersen. "Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages". ESAIM: Probability & Statistics. 2019, 23. 803-822. https://doi.org/10.1051/ps/2019008

Vancouver

Nielsen MS, Pedersen J. Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages. ESAIM: Probability & Statistics. 2019;23:803-822. doi: 10.1051/ps/2019008

Author

Nielsen, Mikkel Slot ; Pedersen, Jan. / Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages. I: ESAIM: Probability & Statistics. 2019 ; Bind 23. s. 803-822.

Bibtex

@article{156e56f3e8a34b25bff646abe9baf0cb,
title = "Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages",
abstract = "The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such quantities in the case where the stationary process is a discretely sampled continuous-time moving average driven by a L{\'e}vy process. We obtain sufficient conditions, in terms of the kernel of the moving average and the coefficients of the quadratic form, ensuring that the centered and adequately normalized version of the quadratic form converges weakly to a Gaussian limit.",
keywords = "DRIVEN, Levy processes, Limit theorems, RANDOM-VARIABLES, moving averages, quadratic forms",
author = "Nielsen, {Mikkel Slot} and Jan Pedersen",
year = "2019",
doi = "10.1051/ps/2019008",
language = "English",
volume = "23",
pages = "803--822",
journal = "ESAIM: Probability & Statistics",
issn = "1292-8100",
publisher = "E D P Sciences",

}

RIS

TY - JOUR

T1 - Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages

AU - Nielsen, Mikkel Slot

AU - Pedersen, Jan

PY - 2019

Y1 - 2019

N2 - The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such quantities in the case where the stationary process is a discretely sampled continuous-time moving average driven by a Lévy process. We obtain sufficient conditions, in terms of the kernel of the moving average and the coefficients of the quadratic form, ensuring that the centered and adequately normalized version of the quadratic form converges weakly to a Gaussian limit.

AB - The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such quantities in the case where the stationary process is a discretely sampled continuous-time moving average driven by a Lévy process. We obtain sufficient conditions, in terms of the kernel of the moving average and the coefficients of the quadratic form, ensuring that the centered and adequately normalized version of the quadratic form converges weakly to a Gaussian limit.

KW - DRIVEN

KW - Levy processes

KW - Limit theorems

KW - RANDOM-VARIABLES

KW - moving averages

KW - quadratic forms

U2 - 10.1051/ps/2019008

DO - 10.1051/ps/2019008

M3 - Journal article

VL - 23

SP - 803

EP - 822

JO - ESAIM: Probability & Statistics

JF - ESAIM: Probability & Statistics

SN - 1292-8100

ER -