I'm fitting a GARCH(1,1) model to some data:
$Y_{t} = \sigma_{t}\epsilon_{t}$ with $\epsilon_{t} \sim t(\nu)$,
$\sigma_{t}^{2} = a_{0} + a_{1}Y_{t-1}^{2} + b_{1}\sigma_{t-1}^{2}$.
Estimating the parameters and standard errors I get a p-value of approx. 0.26 for $a_{0}$. Now, $\hat a_{0}$ is very close to zero. I can't seem to fit the model without the constant in R, so I'm wondering whether it would be alright to proceed working with the model.
Plots of the ACF/PACF of the squared standardized residuals suggest a good fit (the other estimates are significant at the 5% level (one of them barely)).
Cheers!