I am implementing a program to fit an ARMA-GARCH model to given data.
My model parameters are optimised by maximizing the Maximum Likelihood function using a nonlinear algorithm.
The algorithm requires an initial set of parameter values to start from, and I noticed by looking at other GARCH tools out there that those initial parameters have a huge impact on the result.
How can I choose those initial parameter values for my model?
I know for instance that for an AR model we can use Yule-Walker equations or OLS, but I am not sure about an ARMA-GARCH process.