Why are my forecast intervals so large? (ARIMA)

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. 