1. ARIMA diagnostics
Diagnostics for ARIMA models is no different than doing it for ARMA models.
We'll look at an example and consider overfitting. That is, once a model seems reasonable, you can try adding a parameter to see if doing so makes a difference. If there is a difference, then you change your model. Otherwise, you are done.
2. Weekly Oil Prices ARIMA(1, 1, 1)?
In the previous video we looked at weekly oil prices in the US from 2000 to 2006. To remove the trend, we differenced the data.
3. Weekly Oil Prices ARIMA(1, 1, 1)?
Then the ACF and PACF appear to be tailing off, so we considered fitting an ARIMA(1,1,1).
4. Weekly Oil Prices ARIMA(1, 1, 1)?
Using sarima, we fit an ARIMA(1,1,1) to the oil price series. Here are the parameter estimates, and they are significant.
5. Weekly Oil Prices ARIMA(1, 1, 1)!
The residual analysis looks fine too.
6. Overfit: ARIMA(2, 1, 1) and ARIMA(1, 1, 2)
Now we can try to add an AR parameter and then an MA parameter to see if it makes a difference. In each case, the additional parameter is not significant and the other parameters are practically unchanged.
Hence our original model ARIMA(1,1,1) fits well.
7. Let's practice!