How are the upper bounds and lower bounds calculated

[Krishna Sangeeth KS]

Hi,

I am trying to figure out how the upper bound and lower bounds are calculated in statsmodels for forecasting modules such as exponential smoothing based on prediction interval. 

Any pointers on this will be really useful for me. 

Best,

Krishna

[Kevin Sheppard]

You compute the forecast error variance, which depends on the model and estimated parameters, and then the interval is +/- 1.96 * sqrt(var(t+h)) where h is the number of steps ahead. You should look up forecast error variance for ARIMA models to understand how this value is calculated.  It requires constructing the impulse function.