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On the Finite-Sample Accuracy of Nonparametric Resampling Algorithms for Economic Time Series

  • Berkowitz, J.
  • Birgean, I.
  • Kilian, L.

In recent years, there has been increasing interest in nonparametric bootstrap inference for economic time series. Nonparametric resampling techniques help protect against overly optimistic inference in time series models of unknown structure. They are particularly useful for evaluating the fit of dynamic economic models in terms of their spectra, impulse responses, and related statistics, because they do not require a correctly specified economic model. Notwithstanding the potential advantages of nonparametric bootstrap methods, their reliability in small samples is questionable. In this paper, we provide a benchmark for the relative accuracy of several nonparametric resampling algorithms based on ARMA representations of four macroeconomic time series. For each algorithm, we evaluate the effective coverage accuracy of impulse response and spectral density bootstrap confidence intervals for standard sample sizes. We find that the autoregressive sieve approach based on the encompassing model is most accurate. However, care must be exercised in selecting the lag order of the autoregressive approximation.

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Paper provided by Michigan - Center for Research on Economic & Social Theory in its series Papers with number 99-01.

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Length: 58 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:fth:michet:99-01

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  1. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  2. Diebold, Francis X & Kilian, Lutz, 2000. "Measuring Predictability: Theory And Macroeconomic Applications," CEPR Discussion Papers 2424, C.E.P.R. Discussion Papers.
  3. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR (∞) Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 309-332, May.
  4. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1998. "Modeling Money," NBER Working Papers 6371, National Bureau of Economic Research, Inc.
  5. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
  6. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June.
  7. Bühlmann, Peter, 1995. "The blockwise bootstrap for general empirical processes of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 247-265, August.
  8. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361 National Bureau of Economic Research, Inc.
  9. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
  10. Diebold, Francis X & Ohanian, Lee E & Berkowitz, Jeremy, 1998. "Dynamic Equilibrium Economies: A Framework for Comparing Models and Data," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 433-51, July.
  11. Hirotugu Akaike, 1969. "Power spectrum estimation through autoregressive model fitting," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 407-419, December.
  12. Julio J. Rotemberg & Michael Woodford, 1998. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy: Expanded Version," NBER Technical Working Papers 0233, National Bureau of Economic Research, Inc.
  13. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  14. Robert G. King & Mark W. Watson, 1995. "Money, prices, interest rates and the business cycle," Working Paper Series, Macroeconomic Issues 95-10, Federal Reserve Bank of Chicago.
  15. Kilian, L., 1998. "Pitfalls in Constructing Bootstrap Confidence Intervals for Asymptotically Pivotal Statistics," Papers 98-04, Michigan - Center for Research on Economic & Social Theory.
  16. Kilian, L. & Bergean, I., 1999. "Data-Driven Nonparametric Spectral Density Estimators for Economic Time Series: A Monte Carlo Study," Papers 99-04, Michigan - Center for Research on Economic & Social Theory.
  17. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  18. Diebold, F.X. & Kilian, L. & Nerlove, Marc, 2006. "Time Series Analysis," Working Papers 28556, University of Maryland, Department of Agricultural and Resource Economics.
  19. 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.
  20. Kilian, Lutz, 2001. "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(3), pages 161-79, April.
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