Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation
Files
Published version
Date
2007-11-01
Authors
Pipiras, Vladas
Abry, Patrice
Taqqu, Murad S.
Version
OA Version
Citation
Vladas Pipiras, Murad S Taqqu, Patrice Abry. 2007. "Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation." BERNOULLI, v. 13, Issue 4, pp. 1091 - 1123 (33). https://doi.org/10.3150/07-BEJ6143
Abstract
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence between the stable variables, some of which are new. The bounds are also used to deduce the central limit theorem for unbounded functions of stable moving average time series. This result extends the earlier results of Tailen Hsing and the authors on central limit theorems for bounded functions of stable moving averages. It can be used to show asymptotic normality of wavelet-based estimators of the self-similarity parameter in fractional stable motions.