# Calculating Prediction Intervals for multistep univariate time series forecasting using Bootstrapping

I understand the way to compute the prediction interval at 5% and 95% for one step forward forecast based on Bill's answer to the question at Bootstrap prediction interval. The idea being that based on the residuals in the time series using bootstrapping(replacement with sampling multiple times) one can construct the distribution at 5% and 95% percentiles for the first forecast point. What I am struggling to understand is how to calculate the prediction interval for the second point (and other points in the future thereafter). Based on the bootstrap distribution we get one value each of the 5% and 95% percentiles, and the residuals should be added over time

So,

e{5, t+1} = obtained from bootstrap distribution
e{5, t+2} = e{5, t+1} + e{5, t+1}
e{5, t+3} = e{5, t+1} + e{5, t+1} + e{5, t+1}


It will just end up giving a diverging cone with straight lines, and I feel I am missing something here. I am trying to find the prediction intervals solely based on the nature of residuals in historical data and the output that I have from a black-box forecast method. Would love some insights into this