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

Mikkel Slot Nielsen; Jan Pedersen

doi:10.1051/ps/2019008

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

Mikkel Slot Nielsen, Jan Pedersen

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

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 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.

Original language	English
Journal	ESAIM: Probability & Statistics
Volume	23
Pages (from-to)	803-822
Number of pages	20
ISSN	1292-8100
DOIs	https://doi.org/10.1051/ps/2019008
Publication status	Published - 2019

Keywords

DRIVEN
Levy processes
Limit theorems
RANDOM-VARIABLES
moving averages
quadratic forms

Access to Document

10.1051/ps/2019008

https://arxiv.org/pdf/1807.01513.pdf

Cite this

@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",

}

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

SN - 1292-8100

VL - 23

SP - 803

EP - 822

JO - ESAIM: Probability & Statistics

JF - ESAIM: Probability & Statistics

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this