Why are my forecast intervals so large? (ARIMA)

Question

I am trying to perform a forecast on jet fuel prices (from FRED), where i total 260 observations running from jan. 2000 to august 2021 with monthly frequency and no apparant seasonality

From looking at the residuals

it suggests that the ts should be differenced, where an augmented Dickey-fuller test confirms this, as it leaves a test-statistic of -6.71, which is lower than the critical values.

From here I simulated an ARIMA and ARMA function, to find out if the trend is stochastic or determistic running the codes:

model.arima <- auto.arima(y, d=1, seasonal = FALSE, ic = "aic", 
                          stepwise = FALSE, approximation = FALSE, 
                          trace = TRUE)

model.arma <- auto.arima(y, d=0, xreg=1:T, seasonal = FALSE, ic = "aic", 
                         stepwise = FALSE, approximation = FALSE, 
                         trace = TRUE)

screenreg(list(model.arima,model.arma))

By looking at the EIC score, it suggest that an ARIMA(1,1,2) model best describes the relationship, and I will thereby assume that the trend is stochastic, but I find no significant drift.

When running the forecast, where I compare it with a determistic trend (ARMA(3,2) model, I get insanely large forecast intervals

.

Does this make sense? I spoke with my professor, who suggested that the parameters of the model is very small and thereby the intervals is represented a large deal by the error term, which implies that my model is faulty. However, I have no clue on how to fix this.

Answer 1

Your data is noisy, there is no clear pattern. The wide intervals tell you about the uncertainty, the intervals for the predictions are wide because the model is uncertain. If you had a clear, repetitive pattern that could be predicted, they would be narrower. For example, here you can find an example of SARIMA results for such time-series from the great forecasting handbook by Rob Hyndman and George Athanasopoulos.

Wide intervals do not necessarily tell you that the model is faulty. It can be as well that the data is hard to predict, no matter what model you choose. A simple sanity check is to answer yourself if there is any visible pattern in the data, in case of your data it doesn't seem to be the case. In fact, if you had much thinner prediction intervals for the data you're showing, I would expect you to prove me that the model is not overfitting.