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Normal
The EGARCH model is given by,A detailed summary can be found in the Matlab documentation here.If the innovation distribution is normal then,I've figured out that this is true because the expectation is that of the folded normal distribution which is described on the wikipedia page here (just set the mean and standard deviation to zero and it simplifies).I'm therefore assuming that if the EGARCH innovation distribution is student's-t, then the following relation,must be the expectation of the folded Student's-t distribution.I am wondering how you would go about deriving this assuming the standardised Student's-t distribution is given by:From what I can guess, this is two parts:Calculate analytic form of folded Student's-tCalculate (\int_{-{\infty}}^{+{\infty}} xf(x) dx) for the expectation valueand I am stumped by the first part.
The EGARCH model is given by,
A detailed summary can be found in the Matlab documentation here.
If the innovation distribution is normal then,
I've figured out that this is true because the expectation is that of the folded normal distribution which is described on the wikipedia page here (just set the mean and standard deviation to zero and it simplifies).
I'm therefore assuming that if the EGARCH innovation distribution is student's-t, then the following relation,
must be the expectation of the folded Student's-t distribution.
I am wondering how you would go about deriving this assuming the standardised Student's-t distribution is given by:
From what I can guess, this is two parts:
and I am stumped by the first part.
