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The grid bootstrap and the autoregressive model

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  • Hansen,B.E.

    (University of Wisconsin-Madison, Social Systems Research Institute)

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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File URL: http://www.ssc.wisc.edu/~bhansen/papers/grid.pdf
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Bibliographic Info

Paper provided by Wisconsin Madison - Social Systems in its series Working papers with number 26.

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Date of creation: 1998
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Handle: RePEc:att:wimass:199826

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Postal: UNIVERSITY OF WISCONSIN MADISON, SOCIAL SYSTEMS RESEARCH INSTITUTE(S.S.R.I.), MADISON WISCONSIN 53706 U.S.A.

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  1. Diebold, Francis X & Senhadji, Abdelhak S, 1996. "The Uncertain Unit Root in Real GNP: Comment," American Economic Review, American Economic Association, vol. 86(5), pages 1291-98, December.
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  8. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-85, March.
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  11. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  12. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  13. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
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  15. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  16. repec:cup:etheor:v:9:y:1993:i:3:p:363-76 is not listed on IDEAS
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