I am trying to fit an ARFIMA(p,d,q)-GARCH(1,1) model to an asset returns time series. I start with an ARFIMA(0,0,0)-GARCH(1,1). The diagnostics tests like persistence requirement, Ljung Box test for standardised residuals, squared standardised residuals, ARCH LM Test, goodness of fit test all seem to pass.
When I start adding ARFIMA parameters, the Loglikelihood starts increasing (and AIC falling), but in ALL these cases Ljung Box test for standardised residuals fails with very small p-values (even upto ARFIMA(10,d,10)).
My return series is already stationary as per adf test.
I am trying to understand this intuitively. I am not fitting any equation for the mean and modeling only the volatility. Is this ok ? Essentially, if I force an ARMA structure on the time series, I am introducing an auto correlation artificially ?