I am currently writing my thesis about GARCH modeling of a financial return series. More specifically, I first modelled the return $r_t$ within the following equation: $r_t = \epsilon_t$. In other words, I dropped any mean equation (e.g. ARMA) and tried to model the return series solely as a GARCH(1,1). I made all the pretests (ARCH-LM, ..), there are GARCH effects. My estimation also produced highly significant results (see first picture).
However, when predicting the residuals via "predict myresiduals, residuals" and testing them in terms of no more GARCH effects, then tests for autocorrelation etc. all indicate that there still are GARCH effects (i.e. volatility clustering). I then thought maybe I should add an ARMA(1,1) mean equation. I did and I, again, got significant results for both ARMA and GARCH parameters (see picture 2).
But again, when predicting the residuals and testing whether the volatility clustering was taken care of, there is still volatility clustering in the residuals. What do I do wrong?