I am currently building a model based on a GARCH process. You can find a quick description of how the variance is modelled below.
$\sigma_t^2 = \alpha_0 + \sum\limits_{i=1}^{n} \alpha_i \epsilon_{t-1}^2$, $\epsilon_t = \sigma_t z_t$ where $z_t$ is a white noise process
Requirements are that $\alpha_0 >0, \alpha_i \geq 0,i>0$.
The current results show a confidence interval where the lower bound is negative and the upperbound is positive. How should I interpret this lower bound given the requirements for the variance process? Should one prefer a model with a higher BiC score over this model, that is, is it problematic that the confidence interval contains zero? Note that I do not want to simply remove this intercept from the model but that I want to know its implications on the requirement that the intercept should be larger than 0.
