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# Does asymptotic linearity of the regression extend
to stable domains of attraction?

**Renata Cioczek-Georges
**

Murad S. Taqqu

### Abstract:

*Hardin, Samorodnitsky, Taqqu (1991) have
shown that the regression is typically asymptotically linear when is an -stable random vector with . We provide
necessary and
sufficient conditions for asymptotic linearity of where
is an -stable random vector and is
a random variable, independent of
, such that is in the domain of normal attraction
of ***X**.
Asymptotic linearity does not always hold even when is
linear. For some
distributions of , the asymptotic rate of
fluctuates.