# Outliers In Predicted Intervals

In my stats class today, the professor was showing us some output from MINITAB on a prediction interval that was calculated (from time series data). For one of the prediction intervals, MINITAB had an X marked with the statement that there was an outlier in the prediction interval. My recollection is that the prediction interval was actually a prediction interval for some time at which we wanted a forecast into the future.

I searched the MINITAB documentation and can't find a satisfactory explanation for how a computed prediction interval can contain an outlier.

Does anyone know what this means?

TIA, Matt

• What time series model? I've got Minitab 17 handy and if you can provide the model and the data I'll be able to see exactly what you see and help. You can send it to me at mikekr at aol dot com Commented Nov 7, 2014 at 20:07
• I sent you the data file (as an Excel file) which only has 24 data values along with what my professor showed as the output in class. Thank you! Commented Nov 8, 2014 at 20:34

The idea is simple: If you are predicting an observation which is far away from the data you have, your forecast is likely to be awry.

Your model is a simple time series model y = a + b t, where a and b are coefficients and t is time from 1 to 24.

Consider, for example, if you had a similar regression model to predict bus maintenance expenses from bus age, and had data on buses which were 1, 2, 3 .... 10 years old. You might expect a roughly linear pattern of increasing maintenance costs with age. So far, so good.

You could use this to predict the maintenance cost of an 8 year old bus with no problem. Going outside the range, though, can be a problem. You're probably OK predicting an 11 year old bus, or a 12 year old bus, but you wouldn't expect this to be valid for an 80 year old bus -- that's too far outside the range of the data.

That's what's happening here. Your data are times from 1 to 24, and once you get to predicting 28, it triggers Minitab's decision rule for deciding that your value of x is too far out from your actual values and you should be cautious.

A similar thing happens if we predict backwards in time. Minitab is OK predicting 0 (one month before your data series starts with 1), -1 and -2, but when we get to -3 and -4 we get the same flag that you got when we got to period 28.

Unfortunately, neither in the Minitab documentation nor in the online help can I find the explicit rule used; there are some hints that it involves leverage and the hat matrix, but nothing definitive for the Predict module. I've sent these snippets of documentation back to you in an email. Hope this helps.

• Hi, This is what I had thought, since as the PI goes out from Xbar, it fans out and eventually will get "too large" according to some criterion (which as you say, is somewhat vague and undefined). I very much appreciate your help: at least I know it is not something that I missed, and is just a routine in MINITAB which is not well documented. Commented Nov 9, 2014 at 18:12