Tail index in dependent data

Antonella Altamura and Marco Bee spotted that the language of the discussion on tail index for ARCH type data was not correct. It said that

\begin{equation*} \Gamma(\iota/2+1/2)=\sqrt{\pi}(2\alpha)^{-\iota/2} \end{equation*} was the unconditional distribution of \( Y \) which of course does not make sense.

Instead it should say that the value of \(\iota\) can be found by solving for \(\iota\) in the equation.