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Pitfalls in Constructing Bootstrap Confidence Intervals for Asymptotically Pivotal Statistics

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  • Kilian, L.

Abstract

The conventional Edgeworth expansion view of bootstrap confidence intervals suggests that for the bootstrap to exceed the accuracy of the normal approximation one must bootstrap asymptotically pivotal statistics. This paper questions the basic premise of the asymptotic theory used to rationalize the higher-order accuracy of bootstrap intervals for asymptotically pivotal statistics. In finite samples, these statistics often are not even approximately pivotal. As a result, Edgeworth expansion arguments for pivotal statistics do not apply, and the only way to compare the accuracy of alternative intervals is by simulation. The paper documents that percentile-t intervals based on asymptotic pivots tend to behave erratically in small samples and may be much less accurate than bootstrap intervals based on nonpivotal statistics. It is also shown that bootstrap intervals can be very accurate in the absence of asymptotic refinements, and that there are huge differences in coverage accuracy among asymptotically equivalent intervals that cannot be explained by Edgeworth expansion arguments.

Suggested Citation

  • Kilian, L., 1998. "Pitfalls in Constructing Bootstrap Confidence Intervals for Asymptotically Pivotal Statistics," Papers 98-04, Michigan - Center for Research on Economic & Social Theory.
  • Handle: RePEc:fth:michet:98-04
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    Citations

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    Cited by:

    1. Berkowitz, J. & Birgean, I. & Kilian, L., 1999. "On the Finite-Sample Accuracy of Nonparametric Resampling Algorithms for Economic Time Series," Papers 99-01, Michigan - Center for Research on Economic & Social Theory.
    2. Gonzalo Camba-Mendez & George Kapetanios, 2002. "Bootstrap Statistical Tests of Rank Determination for System Identification," Working Papers 468, Queen Mary University of London, School of Economics and Finance.
    3. Kapetanios, G. & Weeks, M., 2003. "Non-nested Models and the likelihood Ratio Statistic: A Comparison of Simulation and Bootstrap-based Tests," Cambridge Working Papers in Economics 0308, Faculty of Economics, University of Cambridge.

    More about this item

    Keywords

    TIME SERIES ; ECONOMETRICS;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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