Given the estimate of GARCH(1, 1) model parameters I observe the new price. How to update the estimate with this new information.
Let's assume I know the coefficients that maximize the likelihood given the data up to the time $T$. At time $T+1$ the new price is observed and I wish to update the coefficients without recomputing the full model
I am looking for the asymptotic convergence of the coefficients - at each time step $T$ I am OK to update the coefficients in suboptimal way but I want them to converge to the true values at infinity.