I have the European TTF GAS spot Price time series from 31/12/1990 to 31/10/2022:
I downloaded it from Word Bank:
I would like to model TTS price or return dynamics by a conditional model for the mean and a conditional model for the variance. I found many papers that fit an ARMA(1,1)-GARCH(1,1) to the raw returns, I tried with multiple ARMA(p,q)-GARCH(r,s)-types models with both a Student-t and a Gaussian distributional assumption for the innovations (of course also comparing models according to BIC and AIC), but every times standardized residuals and/or their squared values present some high degree of autocorrelation. For example ARMA(1,0)-GARCH(1,1) assuming Student-t distribution for the innovations gives:
In the figure the second row are standardized residuals and the third are squared standardized residuals. Then I assumed that autocorrelation may be imputable to the seasonal nature of Natural GAS, therefore I deseasonalized log(P) without the dummy-variables approach, but nothing changed. How can Natural GAS TTF spot price be modeled?
Thank you in advance.