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.