IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v17y2001i1p83-103.html
   My bibliography  Save this article

Effects of parameter estimation on prediction densities: a bootstrap approach

Author

Listed:
  • Pascual, Lorenzo
  • Romo, Juan
  • Ruiz, Esther

Abstract

In this paper, we study the impact of parameter estimation on prediction densities using a bootstrap strategy to estimate these densities. We focus on seasonal ARlMA processes with possibly non normal innovations. We compare prediction densities obtained using the Box and Jenkins approach with bootstrap densities which may be constructed taking into account parameter estimation variability (PRR) or using parameter estimates as if they were the true parameters (CB). By means of Monte Carlo experiments, we show that the average coverage of the intervals is closer to the nominal value when intervals are constructed incorporating parameter uncertainty. The effects of parameter estimation are particularly important for small sample sizes and when the error distribution is not Gaussian. We also analyze the effect of the estimation method on the shape of prediction densities comparing prediction densities constructed when the parameters are estimated by OLS and by LAD. We show how, when the error distribution is not Gaussian, the average coverage and length of intervals based on LAD estimates are closer to nominal values than those based on OLS estimates. Finally, the performance of the PRR procedure is illustrated with two empirical examples.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
  • Handle: RePEc:eee:intfor:v:17:y:2001:i:1:p:83-103
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169-2070(00)00069-8
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    2. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    3. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    4. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
    5. Victor Gómez & Agustín Maravall, 1996. "Programs TRAMO and SEATS, Instruction for User (Beta Version: september 1996)," Working Papers 9628, Banco de España;Working Papers Homepage.
    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. Ng, Jason & Forbes, Catherine S. & Martin, Gael M. & McCabe, Brendan P.M., 2013. "Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 411-430.
    2. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
    3. Tae-Hwy Lee & Yong Bao & Burak Saltoğlu, 2007. "Comparing density forecast models Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003;," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 203-225.
    4. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Michael Wolf & Dan Wunderli, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 352-376, May.
    5. Konstantinidi, Eirini & Skiadopoulos, George, 2011. "Are VIX futures prices predictable? An empirical investigation," International Journal of Forecasting, Elsevier, vol. 27(2), pages 543-560.
    6. 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.
    7. Gonçalves Mazzeu, Joao Henrique & Ruiz, Esther & 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.
    8. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2005. "Bootstrap prediction intervals for power-transformed time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 219-235.
    9. Alonso Fernández, Andrés Modesto & Bastos, Guadalupe & García-Martos, Carolina, 2017. "BIAS correction for dynamic factor models," DES - Working Papers. Statistics and Econometrics. WS 24029, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Andres Alonso & Juan Romo, 2005. "Forecast of the expected non-epidemic morbidity of acute diseases using resampling methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(3), pages 281-295.
    11. Reeves, Jonathan J., 2005. "Bootstrap prediction intervals for ARCH models," International Journal of Forecasting, Elsevier, vol. 21(2), pages 237-248.
    12. Goulas, Lambros & Skiadopoulos, George, 2012. "Are freight futures markets efficient? Evidence from IMAREX," International Journal of Forecasting, Elsevier, vol. 28(3), pages 644-659.
    13. Matei Demetrescu, 2007. "Optimal forecast intervals under asymmetric loss," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(4), pages 227-238.
    14. Alonso, Andrés M. & Romo, Juan, 2001. "Forecast of the expected non-epidemic morbidity of acute diseases using resampling methods," DES - Working Papers. Statistics and Econometrics. WS ws013422, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. 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.
    16. Alonso, Andres M. & Sipols, Ana E., 2008. "A time series bootstrap procedure for interpolation intervals," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1792-1805, January.
    17. 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.
    18. 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.
    19. Atanasios Mitropoulos, 2001. "On the Measurement of the Predictive Success of Learning Theories in Repeated Games," Experimental 0110001, EconWPA.
    20. 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.
    21. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    22. 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.
    23. Clements, Michael P. & Taylor, Nick, 2001. "Bootstrapping prediction intervals for autoregressive models," International Journal of Forecasting, Elsevier, vol. 17(2), pages 247-267.
    24. Andrés Alonso & Daniel Peña & Juan Romo, 2006. "Introducing model uncertainty by moving blocks bootstrap," Statistical Papers, Springer, vol. 47(2), pages 167-179, March.
    25. 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.

    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:eee:intfor:v:17:y:2001:i:1:p:83-103. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.