Bootstrapping empirical distribution functions of residuals from autoregressive model fitting

X = {X(i)} is a stationary autoregressive model of order p. Data X(i), i = -p + 1, -p + 2,..., n is collected, and r(i,n) are the residuals after model fitting. F-n(x) is the empirical distribution function of the residuals. Suppose the innovations sequence has distribution F, bounded density f and four finite moments. Under these conditions the process root n(F-n(F-1(t)) - t) converges weakly to a Gaussian process, which depends on the density f. The limit process is not distribution free. Bootstrapping an AR process from the raw EDF does not work. A method of estimating quantiles, based on a smoothed EDF bootstrap, is considered. A numerical study of the method is made.