Finding the conditional variance and CDF

  • #1
Usagi
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Question: Assume a bivariate GARCH process as follows:


where:

is the conditional standard deviation of

is the conditional standard deviation of

is the conditional correlation between and

are the shocks that drive the system. The shocks are independent and identically distributed and have zero mean, unit variance and zero covariance. However they are not necessarily independent of each other. The distribution is unspecified.

From Eqns. and we have:



Define as:



or equivalently,

----------

Need clarification #1: The question then goes on to state: In the special case where the conditional mean function of is linear in , the first two conditional moments of , given , can be expressed as:



Where does the expression come from? How do you derive this expression?

Need clarification #2: The question continues to state: Consider , the conditional (location-scale) demeaned and standardized cdf of such that:



Then Eqn. can be expressed as:



Where does Eqn. come from? How do you derive it?

Thanks in advance!
 

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