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I would like to predict prediction interval for a SAR model (function errorsarlm in R - package spdep). While the function predict.lm allows to set interval='prediction' parameter to predict the upper and lower boundary of predictions, the function predict.sarlm does not. Is it because it is incorrect to estimate the prediction interval of a SAR or simply because it hasn't implemented? Is it possible to calculate those prediction intervals manually? Below a replicable example:

library(spdep)
data(oldcol)
lw <- nb2listw(COL.nb, style="W") #listw object
mod <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw) #SAR model
predict(mod, COL.OLD) #here I would like to get prediction intervals
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