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The Grid Bootstrap And The Autoregressive Model

  • Bruce E. Hansen

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 © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

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Article provided by MIT Press in its journal The Review of Economics and Statistics.

Volume (Year): 81 (1999)
Issue (Month): 4 (November)
Pages: 594-607

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Handle: RePEc:tpr:restat:v:81:y:1999:i:4:p:594-607
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  1. 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.
  2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  3. J. Carpenter, 1999. "Test inversion bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 159-172.
  4. 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.
  5. Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
  6. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  7. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  8. Knight, J.L. & Satchell, S.E., 1993. "Asymptotic Expansions for Random Walks with Normal Errors," Econometric Theory, Cambridge University Press, vol. 9(03), pages 363-376, June.
  9. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  10. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
  11. repec:cup:etheor:v:9:y:1993:i:3:p:363-76 is not listed on IDEAS
  12. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  13. 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.
  14. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  15. Nankervis, John C & Savin, N E, 1996. "The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 161-68, April.
  16. 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.
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