Properties of spectral covariance for linear processes with infinite variance
- 79 Downloads
We consider a measure of dependence for symmetric α-stable random vectors, which was introduced by the second author in 1976. We demonstrate that this measure of dependence, which we suggest to call the spectral covariance, can be extended to random vectors in the domain of normal attraction of general stable vectors. We investigate the asymptotic of the spectral covariance function for linear stable (Ornstein–Uhlenbeck, log-fractional, linear-fractional) processes with infinite variance and show that, in comparison with the results on the properties of codifference of these processes, obtained two decades ago, the results for the spectral variance are obtained under more general conditions and calculations are simpler.
Keywordsstable random vectors measures of dependence random linear processes stochastic integrals
MSCpimary 60E07 secondary 62G52, 60G60
Unable to display preview. Download preview PDF.
- 6.B. Kodia and B. Garel, Estimation and comparison of signed symmetric covariation coefficient and generalized association parameter for alpha-stable dependence modeling, Commun. Stat., Theory Methods, 2014, doi:10.1080/03610926.2012.730167.Google Scholar
- 13.V. Paulauskas, On α-covariance, long, short, and negative memories for sequences of random variables with infinite variance, 2013, arXiv:1311.0606v1.Google Scholar
- 15.G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes. Models with Infinite Variance, Chapman & Hall, New York, 1994.Google Scholar