# Real future value out of 95% predict interval for ARIMA forecast

When the predicted future value actually materializes, does it matter if it is outside the predict interval?

The value of prediction intervals is that they express the uncertainty in the forecasts. If we only produce point forecasts, there is no way of telling how accurate the forecasts are. However, if we also produce prediction intervals, then it is clear how much uncertainty is associated with each forecast. For this reason, point forecasts can be of almost no value without the accompanying prediction intervals.

-- from Hyndman & Athanasopoulos (2018) OTexts

I have read the definition of predict interval from the book, but I still not sure about the value outside the predict interval. Can I say it is a warning signal or structure change?

The example below

set.seed(123)
ts.sim <- arima.sim(list(order = c(1,0,0), ar = 0.8), n = 200)
ts.plot(ts.sim)

model <- Arima(ts.sim,c(1,0,0),include.mean = FALSE,include.drift = FALSE,method = "ML")
plot(forecast(model,h=20),ylim=c(-8,8))

lines(c(rep(NA,200),5+rnorm(20,0,1)),type="l",col="red")


The red line are out of the 95% predict interval.

Thanks for every help!

• What you are asking about are prediction intervals, not confidence intervals. There is a fundamental difference. Commented Feb 15, 2022 at 12:39
• that chart doesn't look good for your model Commented Feb 15, 2022 at 13:38
• Consider a data transformation as non-normal data (with say fat tails) will, as expected, more often violate the confidence/prediction interval bounds. Commented Feb 15, 2022 at 15:41
• @StephanKolassa - I have made a mistake in there. Thanks for the correction.
– Ivan
Commented Feb 16, 2022 at 1:23