Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation

Details Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation

2007-11-28

arxiv.org/abs/0711.4457v1

Bernoulli 2007, Vol. 13, No. 4, 1091-1123

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ6143 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6143

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.

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