I have time series predictions with 50% and 90% confidence intervals. 50% of observations lie below the 50% confidence interval (IIUC, this should happen only 25% of the time), but all observations lie within the 90% confidence interval. Which one should be trusted and why?
Edit: I should add that it's the later observations that are outside the 50% interval and that there are just over 40 observations in total. How many observations should there be in order to trust the intervals?
I think you mean "tolerance intervals" as you are talking about intervals containing a certain proportion of future observations. If they were both calculated correctly, you should "trust" both, but to different degrees. Obviously the 50% interval will not contain as many points as the 90% interval. So, if missing points is important to you, then go with the 90%. However, if achieveing that degree of certainty is too costly, then you will need to use a lower level of coverage. Its really an economic decision of what level of risk you are comfortable with. There is no one-size-fits all answer.