I am relatively new in this field and have my final thesis on crude oil price forecasting. I am stuck in identifying the optimal ARIMA model for my time series. I am using Stata 13. The daily five year series of ICE crude oil futures is shown on a line graph below.


As it is obvious this time series needs differencing which I did after doing the augmented DF test. Here come the issues. I understand ACF and PACF graphs are useful for determining which ARIMA to use, but do I have to apply them to the non stationary series or the differenced one?

Of course I applied both to each series and come up with some weird results I am unsure how to interpret. These can be seen below, first for the original times series, then for the differenced one:



I am unsure what to do next and how to interpret these results and which model would be best to apply. If someone could guide me through to my next move I would be very grateful.

Here is the link to the data in Excel


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    $\begingroup$ Financial price series cannot be predicted based on price alone itself. This is also evident from the ACF that entries are mostly contained within 0.05, which are not significant. The model that will fit best is white noise, which gives you no predictive power. You should also understand that there is no 5 year futures data. Those prices are made up by artificially combining various future contracts. How they are combined also makes a big difference in interpretation. $\endgroup$ Commented Aug 31, 2016 at 18:47

1 Answer 1


"... do I have to apply them to the non stationary series or the differenced one"

@Topli A non-stationary time series is not suitable for time series analysis. Please check the steps for Box-Jenkins Time Series Methodology.

Changing the subject to look at the big picture, I would reconsider using daily values for your problem because daily values are generally very noisy. Try weekly values and more than five years of data.

Remember that differences for lag=1 removes a deterministic trend line. Differences for lag=12 corrects for a seasonal effect within the year using monthly data. I don't know where you live but in USA history, business cycles average close to six years since the early 1940s and almost two years less for 1850s to 1940s even though the old data is crude [not oil :)]. Thus, almost like a seasonal effect, you need enough data to detect the business cycle effect on your series. Thus, more data (time) is always better for time series analysis. I would shoot to see at least four or five business cycles which means you should try to obtain 30 years of data. Also remember that a time series could be subject to external shocks like the several oil crises over the years. If the shocks are severe, you need to break your analysis into parts to exclude the shock because otherwise you will experience discontinuities that weaken your model.


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