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Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages
- Source :
- Nielsen, M S & Pedersen, J 2019, ' Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages ', ESAIM: Probability & Statistics, vol. 23, pp. 803-822 . https://doi.org/10.1051/ps/2019008
- Publication Year :
- 2019
-
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. 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.
- Subjects :
- Statistics and Probability
Stationary process
Gaussian
01 natural sciences
Lévy process
Limit theorems
RANDOM-VARIABLES
quadratic forms
010104 statistics & probability
symbols.namesake
60F05, 60G10, 60G51, 60H05
Moving average
FOS: Mathematics
Applied mathematics
Limit (mathematics)
0101 mathematics
Mathematics
Levy processes
Probability (math.PR)
010102 general mathematics
DRIVEN
Toeplitz matrix
Quadratic form
Kernel (statistics)
symbols
moving averages
Mathematics - Probability
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Nielsen, M S & Pedersen, J 2019, ' Limit theorems for quadratic forms and related quantities of discretely sampled continuous-time moving averages ', ESAIM: Probability & Statistics, vol. 23, pp. 803-822 . https://doi.org/10.1051/ps/2019008
- Accession number :
- edsair.doi.dedup.....a32c8c3079ae3ba8e6d3c9713c332dc2