Advanced

Second-order continuous time moving avaerages via spectral representation

Podgorski, Krzysztof LU and Baxevani, Anastassia (2015) In Working Papers in Statistics
Abstract
The spectral representation of a moving average process obtained as a convolution of a kernel with a general noise measure is studied. A proof of the spectral theorem that yields explicit expression for the spectral measure in terms of the noise measure is presented. The main interest is in noise measures generated by second order Lévy motions. For practical considerations, such measures are easily available through independent sampling. On the other hand spectral measures are not since their increments are dependent, with the notable exception of the Gaussian noise case.



For this reason the issue of approximating the spectral measure by independent increments of the noise is also addressed. For the purpose of... (More)
The spectral representation of a moving average process obtained as a convolution of a kernel with a general noise measure is studied. A proof of the spectral theorem that yields explicit expression for the spectral measure in terms of the noise measure is presented. The main interest is in noise measures generated by second order Lévy motions. For practical considerations, such measures are easily available through independent sampling. On the other hand spectral measures are not since their increments are dependent, with the notable exception of the Gaussian noise case.



For this reason the issue of approximating the spectral measure by independent increments of the noise is also addressed. For the purpose of approximating the moving average process through sums of trigonometric functions, the mean square error of discretization of the spectral representation is assessed. For a specified accuracy, the coefficients of approximation are explicitly given. The method is illustrated for moving averages processes driven by Laplace motion. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
generalized Laplace distribution, moving average processes, weakly stationary
in
Working Papers in Statistics
issue
7
pages
15 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
6d077014-ae62-4764-ad24-27c7f10923f5 (old id 8052684)
alternative location
http://journals.lub.lu.se/index.php/stat/article/view/15038
date added to LUP
2015-10-07 13:39:10
date last changed
2016-04-16 10:21:59
@misc{6d077014-ae62-4764-ad24-27c7f10923f5,
  abstract     = {The spectral representation of a moving average process obtained as a convolution of a kernel with a general noise measure is studied. A proof of the spectral theorem that yields explicit expression for the spectral measure in terms of the noise measure is presented. The main interest is in noise measures generated by second order Lévy motions. For practical considerations, such measures are easily available through independent sampling. On the other hand spectral measures are not since their increments are dependent, with the notable exception of the Gaussian noise case.<br/><br>
<br/><br>
For this reason the issue of approximating the spectral measure by independent increments of the noise is also addressed. For the purpose of approximating the moving average process through sums of trigonometric functions, the mean square error of discretization of the spectral representation is assessed. For a specified accuracy, the coefficients of approximation are explicitly given. The method is illustrated for moving averages processes driven by Laplace motion.},
  author       = {Podgorski, Krzysztof and Baxevani, Anastassia},
  keyword      = {generalized Laplace distribution,moving average processes,weakly stationary},
  language     = {eng},
  number       = {7},
  pages        = {15},
  publisher    = {ARRAY(0x95d4c20)},
  series       = {Working Papers in Statistics},
  title        = {Second-order continuous time moving avaerages via spectral representation},
  year         = {2015},
}