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.
Accepté le :
DOI : 10.1051/ps/2019008
Mots-clés : Limit theorems, Lévy processes, moving averages, quadratic forms
@article{PS_2019__23__803_0,
author = {Nielsen, Mikkel Slot and Pedersen, Jan},
title = {Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages},
journal = {ESAIM: Probability and Statistics},
pages = {803--822},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2019008},
mrnumber = {4045543},
zbl = {1506.60035},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2019008/}
}
TY - JOUR AU - Nielsen, Mikkel Slot AU - Pedersen, Jan TI - Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages JO - ESAIM: Probability and Statistics PY - 2019 SP - 803 EP - 822 VL - 23 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2019008/ DO - 10.1051/ps/2019008 LA - en ID - PS_2019__23__803_0 ER -
%0 Journal Article %A Nielsen, Mikkel Slot %A Pedersen, Jan %T Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages %J ESAIM: Probability and Statistics %D 2019 %P 803-822 %V 23 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2019008/ %R 10.1051/ps/2019008 %G en %F PS_2019__23__803_0
Nielsen, Mikkel Slot; Pedersen, Jan. Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 803-822. doi : 10.1051/ps/2019008. http://www.numdam.org/articles/10.1051/ps/2019008/
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