# How to determine the Forecast Interval beyond the next period.

I like to establish a confidence interval my custom-made forecasting model (not one of the standard ones in the forecast package, which include the interval). The empirical record indicates that the forecast errors are normal distributed and thus I can take the point forecast and calculate intervals like you would do with regular normal distribution intervals:

mean +/- z * sqrt(mean squared error)


Can anybody shine some light on what the appropriate way is for treading the error when making forecasts for periods beyond the immediate future?

• Jochem, you don't supply enough information in your question to allow people to supply reasonable answers. Although forecast errors might have normal distributions, the crux of the matter is to determine how the means and variances of those errors depend on the forecast horizon. I'm afraid your bounty will have been wasted unless you can supply enough details of your model to let people figure this out. If I am mistaken in this assessment, then please explain more clearly what you mean by "trea[t]ing the error" in your question.
– whuber
Feb 17, 2014 at 15:26

Here is an edited answer. Many people use square root of the forecast horizon to scale the errors in the horizon. This comes from the assumptions of random walks, where the errors in each time step are assumed to be independent, thus the variance will scale linearly with time, and volatility (error) scale with square root of time.

You can check below link for an example: http://people.duke.edu/~rnau/three.htm

Yes, I wanted to comment, I wasn't able to because of 50 point reputation requirement

• Welcome to the site, @adam. This isn't an answer to the OP's question. At best it is a comment. Please only use the "Your Answer" field to provide answers. I recognize it's frustrating, but you will be able to comment anywhere when your reputation >50. Alternatively, you can try to expand this into more of an answer. Since you are new here, you may want to take our tour, which contains information for new users. Feb 17, 2014 at 14:41
• @gung I believe this does answer the question of "shin[ing] some light ... for [treating] the error." However, because it lacks any justification or references it has no credibility. It would be interesting to see what assumptions would lead to making this recommendation valid: could you edit your answer, adam, to clarify these points?
– whuber
Feb 17, 2014 at 15:22
• (+1) The general nature of this answer is a reasonable match to the vagueness of the question; it might not be possible to suggest anything more specific unless the question is clarified.
– whuber
Feb 17, 2014 at 17:32