Log likelihood function for P-EGARCH(1,1)-t needed

[ROSSINL]

Hi,

I am doing research on calendar effects, using a Periodic Exponential GARCH(1,1) model with student-t error distribution.
The periodic component is only applied to the constant in the conditional variance equation, by using dummy variables. Please see the mean and conditional variance equation in the attachment (Equations 1).

For example, when I model day-of-the-week effects, S will be equal to 5. Then the significance of the deltas and phis will tell me whether the return and volatility on day i is larger then on the reference day (captured by the constant).

The problem is that I don't know how to specify the log likelihood function. I came as far as the LLF in the attachment under equation 2, but it is only for an EGARCH-t model..so I still miss the periodic component.
Does anyone how to specify the log likelihood function for a P-EGARACH process (with student t errors)?

Thanks!