Conditional moments and linear regression for stable random variables

Gennady Samorodnitsky
Murad S. Taqqu


Jointly -stable random variables with index have only finite moments of order less than , but their conditional moments can be higher than . We provide conditions for this to happen and use the existence of the conditional moments to study the regression . We show that if is a symmetric -stable random vector, then under appropriate conditions, the regression is well-defined even when and is linear in x. The results are applied to different classes of symmetric -stable processes.