Bootstrapped prediction intervals: Quantile, median, SE…?

I am trying to construct prediction intervals for a non linear model via Boostrap. What I do is to apply the usual bootstrap procedure, here you have pseudo-code for 1000 iterations:

for i in 1:1000{
1.- Sample with replacement the in-sample data
2.- Fit the model
3.- Predict out-sample and store results
}

Then once I have the 1000 results of the boostrapped predicted intervals I have the problem that I don't know exactly what to use to construct this interval: if I use the 0.05 and 0.95 quantiles I find that the 0.95 quantile presents very extreme values e.g. 350% deviation from the point forecast, which is not really useful fore the case at hand.

I was thinking on using the median, 0.5 quantile, and just state that the prediction interval deviates the median both for upper and lower bound e.g. if point forecast = 500, median boostrapped distribution = 25 then prediction intervals = c(475,525).

I would appreciate some suggestion on what the best measure or approach is.

• The quantile method has some decent theoretical arguments behind it. I'm not sure why you feel that you can use the median of the bootstrap distribution as a kind of makeshift standard error (what would you do if it was negative?). We all want tighter prediction intervals, but it's not OK to just jury-rig a method. There are different, proper methods for constructing bootstrapped confidence intervals, see for eg. this paper projecteuclid.org/… – einar Feb 14 '17 at 10:17