The grid bootstrap and the autoregressive model

A "grid" bootstrap method is proposed for confidence-interval construction, which has improved performance over conventional bootstrap methods when th e sampling distribution depends upon the parameter of interest. The basic i dea is to calculate the bootstrap distribution over a grid of values of the parameter of interest and form the confidence interval by the no-rejection principle. Our primary motivation is given by autoregressive models, where it is known that conventional bootstrap methods fail to provide correct fi rst-order asymptotic coverage when an autoregressive root is close to unity . In contrast, the grid bootstrap is first-order correct globally in the pa rameter space. Simulation results verify these insights, suggesting that th e grid bootstrap provides an important improvement over conventional method s. Gauss code that calculates the grid bootstrap intervals-and replicates t he empirical work reported in this paper-is available from the author's Web page at www.ssc.wisc.edu similar to bhansen.