Thank you for the answer just to be clear I am actually using garchfit and garchinfer functions in MATLAB but I used these notions since most of people know R here. By any chance do you know that the residuals that I get from garchinfer function is the same as the '@residuals' from "fGarch" in R?

I don't know if this is the place to ask (I didn't want to create redundant questions) but I wonder if a maximum P-value for one-sided is half of the P-value two-sided t-test? To clarify, I am doing a fitting with lsfit function in R but I only want the t-statistic of positive side

Thanks again for your help. Just to be clear, so you mean the maximum P-value for one-sided is half of the P-value two-sided t-test?

Can you help me about how to make this test a one tail (only positive) t-test in lsfit ?

Thanks. The only reason that I am using lsfit is that this is a line in the source code of a function rsFit in fArma package and I am not sure if I can change it?! Can I?