Univariate GARCH(1,1): Which mean eq spec is right?
Posted: Thu Jan 29, 2009 1:22 am
Let's say I try to estimate a univariate GARCH(1,1) with two different specifications of the mean equation.
Specification 1: Mean equation: y_t = Constant + e_t, Variance equation = GARCH(1,1)
Specification 2: Mean equation: y_t = Constant + y_t-1+e_t-1 + e_t , Variance equation = GARCH(1,1)
(Note: the mean equation 1 only contains a constant term and the mean equation 2 is a ARMA(1,1) model.)
Q1: When I change the mean equation from Spec (1) to Spec (2), all residuals or error terms will change accordingly? And, the two variance GARCH(1,1) equations provide completely different estimates?
Q2. If so, how do I know which mean equation specification is appropriate?
P.S. I am a self learner and I have not attended any GARCH class or lecture. I apologize if my question is too simple or stupid. Thanks a lot.
Specification 1: Mean equation: y_t = Constant + e_t, Variance equation = GARCH(1,1)
Specification 2: Mean equation: y_t = Constant + y_t-1+e_t-1 + e_t , Variance equation = GARCH(1,1)
(Note: the mean equation 1 only contains a constant term and the mean equation 2 is a ARMA(1,1) model.)
Q1: When I change the mean equation from Spec (1) to Spec (2), all residuals or error terms will change accordingly? And, the two variance GARCH(1,1) equations provide completely different estimates?
Q2. If so, how do I know which mean equation specification is appropriate?
P.S. I am a self learner and I have not attended any GARCH class or lecture. I apologize if my question is too simple or stupid. Thanks a lot.