# Autocorrelation in residuals of mean model to be used in a GARCH model

My question is related to the autocorrelation present in the mean-model (which is an ARMA process), which will be used in a GARCH model. Is it ok to have autocorrelations in the residuals of the mean-model, given that it will be used in a GARCH model, which by robust standard errors takes care of the residuals in the variance model?

I have edited my question a bit and attached the ACF and PACF plots of the residuals of the ARMA process with AR=11, MA=6, and zero mean. Via an algorithm, this was the model with the lowest AIC value. Using checkresiduals in R, the Ljung-Box test figures are:

data: Residuals from ARIMA(11,0,6) with zero mean Q* = 23.228, df = 3, p-value = 3.619e-05

Model df: 17. Total lags used: 20

Based on this, there is autocorrelation present.

Based on these plots, can I consider the model good for a statistically adequate descriptive model and ignore the Ljung-Box result? EDIT: 2

Based on discussions and advice, I am attaching the screen-shot of the output of the model, prescribed by auto.arima. It gives an optimum model of (4,0,4). But when I run the model in the ARIMA function, it shows a convergence problem. The screenshot is given below: The ACF and PACF plots for (4,0,4) are: How do we take care of the convergence issue? Is it ok to accept the model?

The original log return series is: EDIT: 3

The ACF & PACF of the return series is given below: Update: From the edit of the original post, we get to know the time series of interest is oil price. A decent approximation might be ARIMA(0,1,0). If that yields highly autocorrelated residuals, try auto.arima for a potentially different model. ARIMA(11,0,6) makes little sense to me; I suspect this is a highly overfitted model. But if we were to examine its residuals out of curiosity, I would say the ACF and PACF plots look fairly innocuous (except that the two plots seem to be identical; that might be a mistake). Whether you should trust Ljung-Box test over eyeballing the plots is a contentious question. You probably should not; see Testing for autocorrelation: Ljung-Box versus Breusch-Godfreyor a criticism of the use of the Ljung-Box test on residuals from an ARIMA model.
• @JyotiNair, there is a reason why auto.arima excludes lags above 5; such complex models rarely tend to do particularly well (at least in terms of forecasting) and are prone to overfitting. ARIMA(11,0,6) is quite extreme in that regard. Now I am not saying it is definitely a poor model, but I would trust a simpler model more. As a side note, it is always good to plot the original series in addition to ACF and PACF. You may consider including such a plot in your post. Mar 14 at 7:33