ABSTRACT
While the variance of this expression can be estimated analytically, note that in constructing confidence intervals, a central limit theorem does not ensure normality: the second term of (4) may tend to the normal distribution as n grows large, but the first will only be normal if the disturbances themselves are normal. To deal with this nonnormality is difficult analytically but is straightfonvard using the bootstrap. Following Freedman and Peters (l 984a, 1984b), we bootstrap just as above only we focus on the forecast Xn+tS*J as the statistic of interest. We then calculate a "simulated actual" by adding an additional single bootstrapped residual to the actual forecast Xn+l S. The difference between the forecast and the simulated actual is the simulated forecast error; we obtain an estimate of the probability distribution of the forecast enor by repeating the process B times.
