The Grid Bootstrap and the Autoregressive Model

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Abstract
A "grid" bootstrap method is proposed for confidence-interval construction, which has improved performance over conventional bootstrap methods when the sampling distribution depends upon the parameter of interest. The basic idea 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 first-order asymptotic coverage when an autoregressive root is close to unity. In contrast, the grid bootstrap is first-order correct globally in the parameter space. Simulation results verify these insights, suggesting that the grid bootstrap provides an important improvement over conventional methods. Gauss code that calculates the grid bootstrap intervals - and replicates the empirical work reported in this paper - is available from the author's Web page at www.ssc.wisc.edu~bhansen. © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

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