IDEAS home Printed from https://ideas.repec.org/p/att/wimass/199826.html
   My bibliography  Save this paper

The grid bootstrap and the autoregressive model

Author

Listed:
  • 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
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hansen,B.E., 1998. "The grid bootstrap and the autoregressive model," Working papers 26, Wisconsin Madison - Social Systems.
  • Handle: RePEc:att:wimass:199826
    as

    Download full text from publisher

    File URL: http://www.ssc.wisc.edu/~bhansen/papers/grid.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. 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 463-485, March.
    3. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, October.
    4. 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.
    5. Paul H. Garthwaite & Stephen T. Buckland, 1992. "Generating Monte Carlo Confidence Intervals by the Robbins–Monro Process," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 159-171, March.
    6. 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.
    7. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    8. Knight, J.L. & Satchell, S.E., 1993. "Asymptotic Expansions for Random Walks with Normal Errors," Econometric Theory, Cambridge University Press, vol. 9(3), pages 363-376, June.
    9. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    10. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, October.
    11. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    12. repec:cup:etheor:v:9:y:1993:i:3:p:363-76 is not listed on IDEAS
    13. 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.
    14. 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 161-168, April.
    15. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
    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.
    17. Romano, Joseph P. & Wolf, Michael, 1998. "Subsampling confidence intervals for the autoregressive root," DES - Working Papers. Statistics and Econometrics. WS 6268, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. 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 1291-1298, December.
    19. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    20. 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.
    21. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    2. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    3. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    4. Marcet, Albert & Jarociński, Marek, 2010. "Autoregressions in small samples, priors about observables and initial conditions," Working Paper Series 1263, European Central Bank.
    5. Josep Lluís Carrion-i-Silvestre & María Dolores Gadea & Antonio Montañés, 2017. "“Unbiased estimation of autoregressive models forbounded stochastic processes," AQR Working Papers 201710, University of Barcelona, Regional Quantitative Analysis Group, revised Dec 2017.
    6. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    7. Kim, Jae & Choi, In, 2015. "Unit Roots in Economic and Financial Time Series: A Re-Evaluation based on Enlightened Judgement," MPRA Paper 68411, University Library of Munich, Germany.
    8. Claudio Michelacci, 1999. "Cross-Sectional Heterogeneity and the Persistence of Aggregate Fluctuations," Working Papers wp1999_9906, CEMFI.
    9. Jae H. Kim & In Choi, 2017. "Unit Roots in Economic and Financial Time Series: A Re-Evaluation at the Decision-Based Significance Levels," Econometrics, MDPI, vol. 5(3), pages 1-23, September.
    10. Pesavento, Elena & Rossi, Barbara, 2007. "Impulse response confidence intervals for persistent data: What have we learned?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2398-2412, July.
    11. Kruse, Yves Robinson & Kaufmann, Hendrik, 2015. "Bias-corrected estimation in mildly explosive autoregressions," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112897, Verein für Socialpolitik / German Economic Association.
    12. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    13. Michelacci, Claudio, 2004. "Cross-sectional heterogeneity and the persistence of aggregate fluctuations," Journal of Monetary Economics, Elsevier, vol. 51(7), pages 1321-1352, October.
    14. Kim, Jae H., 2003. "Forecasting autoregressive time series with bias-corrected parameter estimators," International Journal of Forecasting, Elsevier, vol. 19(3), pages 493-502.
    15. Josep Lluís Carrion‐i‐Silvestre & María Dolores Gadea & Antonio Montañés, 2021. "Nearly Unbiased Estimation of Autoregressive Models for Bounded Near‐Integrated Stochastic Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(1), pages 273-297, February.
    16. Claude Lopez & Christian J. Murray & David H. Papell, 2013. "Median-unbiased estimation in DF-GLS regressions and the PPP puzzle," Applied Economics, Taylor & Francis Journals, vol. 45(4), pages 455-464, February.
    17. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    18. Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    19. Diebold, Francis X & Kilian, Lutz, 2000. "Unit-Root Tests Are Useful for Selecting Forecasting Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 265-273, July.
    20. Ernst, Matthew & Rodecker, Jared & Luvaga, Ebby & Alexander, Terence & Kliebenstein, James & MIRANOWSKI, JOHN A, 1999. "The Viability of Methane Production by Anaerobic Digestion on Iowa Swine Farms," ISU General Staff Papers 199910010700001329, Iowa State University, Department of Economics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:att:wimass:199826. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ailsenne Sumwalt (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.