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

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

model <- Arima(ts.sim,c(1,0,0),include.mean = FALSE,include.drift = FALSE,method = "ML")


enter image description here

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

Thanks for every help!

  • 3
    $\begingroup$ What you are asking about are prediction intervals, not confidence intervals. There is a fundamental difference. $\endgroup$ Feb 15, 2022 at 12:39
  • $\begingroup$ that chart doesn't look good for your model $\endgroup$
    – Aksakal
    Feb 15, 2022 at 13:38
  • $\begingroup$ Consider a data transformation as non-normal data (with say fat tails) will, as expected, more often violate the confidence/prediction interval bounds. $\endgroup$
    – AJKOER
    Feb 15, 2022 at 15:41
  • $\begingroup$ @StephanKolassa - I have made a mistake in there. Thanks for the correction. $\endgroup$
    – Ivan
    Feb 16, 2022 at 1:23

1 Answer 1


Your question is whether the points outside the prediction interval indicate a warning signal or structure change. While I am not sure about what you mean by "warning signal" and by "structural change", I figure that you want to know how to interpret data outside the prediction interval.

Well, let's say your prediction interval should contain the new value with a probability of 0.95. Then that means, that you should see about one out of 20 points to be outside the interval, and that would be nothing to worry about. But If there are, in some time interval, clearly more than 5% outside the prediction interval, then this is probably a "structure change". So the red line you plotted would definitely be something to worry about.

  • $\begingroup$ Thank you for your reply. Yes, I want to understand what it means when the value outside the predict interval, because my job needs to monitor and forecast some signals (usually forecast for a year), these signals are mostly stable so the future realized values ​​usually within the predict interval, But sometimes still some value outside the predict interval, and I want to know how to confirm whether the original prediction model is still valid. $\endgroup$
    – Ivan
    Feb 16, 2022 at 1:57

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