For my thesis I first need to examine nine financial time series and fit a conditional volatility model such that the obtained standardized residuals ($z_t = \epsilon_t / \sigma_t$) are approximately iid with mean 0 and variance 1.
Whereas GARCH(1,1) succeeds in delivering iid standardized residuals for five of these series, and GJR-GARCH(1,1) achieves iid standardized residuals for other two series, I've not been able to get iid $z_t$ for the remaining two series using GARCH, GJRGARCH, ThresholdGARCH, EGARCH, NAGARCH and CSGARCH.
When I shared my results with my thesis supervisor, he said I've probably done something wrong since GARCH, GJRGARCH and ThresholdGARCH usually succeed wrt this goal. The problem is I don't understand what I could have done wrong.
The mentioned series are three SPDR ETFs (XLF and XLU). Closing prices can be found here (this is my first question, so I'm sorry if this isn't the way you're supposed to share data):
After obtaining log returns and demeaning them, I use the first 1766 observations to estimate all parameters and obtain standardized residuals. I then conduct ARCH tests on standardized residuals (at lags 1, 5, and 10), which for these two series reject homoscedasticity. Therefore I don't obtain iid residuals and can't go on with my analysis.
Any help would be greatly appreciated.
PS: Is there any other test which is more adequate in testing iid residuals? I think I've read somewhere that, while most people still use ARCH tests on residuals, these are supposed to test raw data and should not be used for residuals.