IDEAS home Printed from https://ideas.repec.org/a/jof/jforec/v23y2004i2p141-154.html
   My bibliography  Save this article

Bias-corrected bootstrap prediction regions for vector autoregression

Author

Listed:
  • Jae H. Kim

    (Department of Econometrics and Business Statistics, Monash University, Caulfield East, Victoria 3145, Australia)

Abstract

This paper examines small sample properties of alternative bias-corrected bootstrap prediction regions for the vector autoregressive (VAR) model. Bias-corrected bootstrap prediction regions are constructed by combining bias-correction of VAR parameter estimators with the bootstrap procedure. The backward VAR model is used to bootstrap VAR forecasts conditionally on past observations. Bootstrap prediction regions based on asymptotic bias-correction are compared with those based on bootstrap bias-correction. Monte Carlo simulation results indicate that bootstrap prediction regions based on asymptotic bias-correction show better small sample properties than those based on bootstrap bias-correction for nearly all cases considered. The former provide accurate coverage properties in most cases, while the latter over-estimate the future uncertainty. Overall, the percentile-t bootstrap prediction region based on asymptotic bias-correction is found to provide highly desirable small sample properties, outperforming its alternatives in nearly all cases. Copyright © 2004 John Wiley & Sons, Ltd.

Suggested Citation

  • Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
    • Handle: RePEc:jof:jforec:v:23:y:2004:i:2:p:141-154
    DOI: 10.1002/for.908
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1002/for.908
    File Function: Link to full text; subscription required
    Download Restriction: no
    File URL: https://libkey.io/10.1002/for.908?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kim, Jae H, 2001. "Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 117-128, January.
    2. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    3. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    4. Kim, Jae H., 1997. "Relationship Between the Forward and Backward Representations of the Stationary VAR Model," Econometric Theory, Cambridge University Press, vol. 13(06), pages 889-889, December.
    5. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
    6. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    7. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    8. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
    9. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    10. Kent D. Wall & David S. Stoffer, 2002. "A State space approach to bootstrapping conditional forecasts in arma models," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 733-751, November.
    11. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2001. "Effects of parameter estimation on prediction densities: a bootstrap approach," International Journal of Forecasting, Elsevier, vol. 17(1), pages 83-103.
    12. 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.
    13. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
    14. Matteo Grigoletto, 1998. "Bootstrap prediction intervals for autoregressive models fitted to non-autoregressive processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(3), pages 285-295, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pascual, Lorenzo & Fresoli, Diego Eduardo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2020. "Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 5-32, March.
    3. Bruns, Martin & Lütkepohl, Helmut, 2022. "Comparison of local projection estimators for proxy vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    4. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.
    5. Tom Engsted & Thomas Q. Pedersen, 2014. "Bias-Correction in Vector Autoregressive Models: A Simulation Study," Econometrics, MDPI, vol. 2(1), pages 1-27, March.
    6. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    7. Winker, Peter & Helmut, Lütkepohl & Staszewska-Bystrova, Anna, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100597, Verein für Socialpolitik / German Economic Association.
    8. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
    9. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Comparison of methods for constructing joint confidence bands for impulse response functions," SFB 649 Discussion Papers 2013-031, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. repec:hum:wpaper:sfb649dp2013-031 is not listed on IDEAS
    11. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
    12. repec:hum:wpaper:sfb649dp2014-007 is not listed on IDEAS
    13. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
    14. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    15. Jing, Li, 2009. "Bootstrap prediction intervals for threshold autoregressive models," MPRA Paper 13086, University Library of Munich, Germany.
    16. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    17. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332, April.
    18. Mulubrhan G. Haile & Lingling Zhang & David J. Olive, 2024. "Predicting Random Walks and a Data-Splitting Prediction Region," Stats, MDPI, vol. 7(1), pages 1-11, January.
    19. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.

    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. Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Clements, Michael P. & Kim, Jae H., 2007. "Bootstrap prediction intervals for autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3580-3594, April.
    3. Kim, Jae H., 2004. "Bootstrap prediction intervals for autoregression using asymptotically mean-unbiased estimators," International Journal of Forecasting, Elsevier, vol. 20(1), pages 85-97.
    4. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
    5. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332, April.
    6. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    7. Jing Li, 2021. "Block bootstrap prediction intervals for parsimonious first‐order vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 512-527, April.
    8. Jing, Li, 2009. "Bootstrap prediction intervals for threshold autoregressive models," MPRA Paper 13086, University Library of Munich, Germany.
    9. Chan, W.S & Cheung, S.H & Wu, K.H, 2004. "Multiple forecasts with autoregressive time series models: case studies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(3), pages 421-430.
    10. Felix Wick & Ulrich Kerzel & Martin Hahn & Moritz Wolf & Trapti Singhal & Daniel Stemmer & Jakob Ernst & Michael Feindt, 2021. "Demand Forecasting of Individual Probability Density Functions with Machine Learning," SN Operations Research Forum, Springer, vol. 2(3), pages 1-39, September.
    11. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    12. Diego Fresoli, 2022. "Bootstrap VAR forecasts: The effect of model uncertainties," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 279-293, March.
    13. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    14. Kim, Jae H. & Wong, Kevin & Athanasopoulos, George & Liu, Shen, 2011. "Beyond point forecasting: Evaluation of alternative prediction intervals for tourist arrivals," International Journal of Forecasting, Elsevier, vol. 27(3), pages 887-901.
    15. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    16. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
    17. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    18. Lorenzo Pascual & Juan Romo & Esther Ruiz, 2004. "Bootstrap predictive inference for ARIMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 449-465, July.
    19. Helmut Lütkepohl, 2010. "Forecasting Aggregated Time Series Variables: A Survey," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2010(2), pages 1-26.
    20. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.

    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:jof:jforec:v:23:y:2004:i:2:p:141-154. 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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    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.