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On the finite-sample accuracy of nonparametric resampling algorithms for economic time series

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  • Jeremy Berkowitz
  • Ionel Birgean
  • Lutz Kilian

Abstract

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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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1999-04.

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Date of creation: 1999
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Handle: RePEc:fip:fedgfe:1999-04

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Keywords: Time-series analysis ; Sampling (Statistics);

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Francis X. Diebold & Lutz Kilian, 1998. "Measuring Predictability: Theory and Macroeconomic Applications," Working Papers 98-16, New York University, Leonard N. Stern School of Business, Department of Economics.
  5. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  7. Diebold, F.X. & Kilian, L. & Nerlove, Marc, 2006. "Time Series Analysis," Working Papers 28556, University of Maryland, Department of Agricultural and Resource Economics.
  8. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1997. "Modeling money," Working Paper Series, Macroeconomic Issues WP-97-17, Federal Reserve Bank of Chicago.
  9. 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.
  10. 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.
  11. 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.
  12. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  13. Francis X. Diebold & Lee E. Ohanian & Jeremy Berkowitz, 1997. "Dynamic equilibrium economies: a framework for comparing models and data," Working Papers 97-7, Federal Reserve Bank of Philadelphia.
  14. 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.
  15. Timothy Cogley & James M. Nason, 1993. "Output dynamics in real business cycle models," Working Papers in Applied Economic Theory 93-10, Federal Reserve Bank of San Francisco.
  16. Kilian, L., 1998. "Pitfalls in Constructing Bootstrap Confidence Intervals for Asymptotically Pivotal Statistics," Papers 98-04, Michigan - Center for Research on Economic & Social Theory.
  17. 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.
  18. Ionel Birgean & Lutz Kilian, 2002. "Data-Driven Nonparametric Spectral Density Estimators For Economic Time Series: A Monte Carlo Study," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 449-476.
  19. 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.
  20. 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.
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Citations

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Cited by:
  1. Gonçalves, Sílvia & Kilian, Lutz, 2002. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Working Paper Series 0196, European Central Bank.
  2. Kilian, Lutz & Rebucci, Alessandro & Spatafora, Nikola, 2009. "Oil shocks and external balances," Journal of International Economics, Elsevier, vol. 77(2), pages 181-194, April.
  3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  4. Bottazzi, G. & Sapio, S. & Secchi, A., 2005. "Some statistical investigations on the nature and dynamics of electricity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 54-61.
  5. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers.
  6. Lutz Kilian & Bruce Hicks, 2013. "Did Unexpectedly Strong Economic Growth Cause the Oil Price Shock of 2003–2008?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(5), pages 385-394, 08.
  7. 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.

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