Interpreation of flat correlogram - ARMA model

I have been asked to build an ARMA model for some oil WTI spot prices.

I have manipulate the data to make it stationary (taking log-returns), and stationarity has been confirmed by the Augmented Dickey Fuller test and all the other stationarity tests available in EViews. However, when I plot out the correlogram to decide about the order of my ARMA, it appears to be almost flat (both the acf and the pacf) and the Q-stat suggest to reject the null of no-autocorrelation for all the lags beyond the first one. All the correlation coefficients appear to be insignificant, using the confidence interval 1.96 + - 1/T^1/2 .

My intuition is that the ARMA model is not a good guess for this kind of data, but I’m struggling to find a scientific justification to my results.

I have thought that the reason for the non-decaying acf and pacf is that the data might be still highly persistent, or that it might have to do with the fact that the manipulated dta doesn't have a unit root but still hasn't got constant variance, but I still struggle to back up my thoughts with solid theory.

Can anybody help me?

Thank you!


Fortran must die
When you say the Q-stat do you mean something like the Box-Ljung test? From what you have said it appears you have no residual Autocorrelation.

Not all series have AR or MA patterns, a random walk or random walk with drift come to mind. I have not heard that certain types of data won't work with ARMA (although some data can be very difficult to analyze correctly in terms of P,D,Q parameters.

If you have a non-decaying ACF or PACF you should not have stationary data. Nor should the Box-Ljung tell you that there is no residual Autocorrelation when there is non-stationary data (as far as I can remember). Seasonality can generate a non-stationary effect, are there any spikes at lags that suggest seasonality in your data?