Volume 23, 2019
|Page(s)||803 - 822|
|Published online||24 December 2019|
Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages
Department of Mathematics, Aarhus University,
Ny Munkegade 118,
* Corresponding author: firstname.lastname@example.org
Accepted: 8 April 2019
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.
Mathematics Subject Classification: 60F05 / 60G10 / 60G51 / 60H05
Key words: Limit theorems / Lévy processes / moving averages / quadratic forms
© EDP Sciences, SMAI 2019
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