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Second-order continuous time moving avaerages via spectral representation

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Author

Summary, in English

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.

Publishing year

2015

Language

English

Publication/Series

Working Papers in Statistics

Issue

7

Document type

Working paper

Publisher

Department of Statistics, Lund university

Topic

  • Probability Theory and Statistics

Keywords

  • generalized Laplace distribution
  • moving average processes
  • weakly stationary

Status

Published