BOOTSTRAPPING UNSTABLE 1ST-ORDER AUTOREGRESSIVE PROCESSES

Consider a first-order autoregressive process X(t) = beta-X(t-1) + epsilon-t, where {epsilon-t} are independent and identically distributed random errors with mean 0 and variance 1. It is shown that when beta = 1 the standard bootstrap least squares estimate of beta-is asymptotically invalid, even if the error distribution is assumed to be normal. The conditional limit distribution of the bootstrap estimate at beta = 1 is shown to converge to a random distribution.