IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/6311.html
   My bibliography  Save this paper

Conditional minimum volume predictive regions for stochastic processes

Author

Listed:
  • Polonik, Wolfgang
  • Yao, Qiwei

Abstract

Motivated by interval/region prediction in nonlinear time series, we propose a minimum volume predictor (MV-predictor) for a strictly stationary process. The MV-predictor varies with respect to the current position in the state space and has the minimum Lebesgue measure among all regions with the nominal coverage probability. We have established consistency, convergence rates, and asymptotic normality for both coverage probability and Lebesgue measure of the estimated MV-predictor under the assumption that the observations are taken from a strong mixing process. Applications with both real and simulated data sets illustrate the proposed methods.

Suggested Citation

  • Polonik, Wolfgang & Yao, Qiwei, 2000. "Conditional minimum volume predictive regions for stochastic processes," LSE Research Online Documents on Economics 6311, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:6311
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/6311/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Ross Askanazi & Francis X. Diebold & Frank Schorfheide & Minchul Shin, 2018. "On the Comparison of Interval Forecasts," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 953-965, November.
    2. Liang, Han-Ying & Peng, Liang, 2010. "Asymptotic normality and Berry-Esseen results for conditional density estimator with censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1043-1054, May.
    3. Laïb Naâmane & Lemdani Mohamed & Ould Saïd Elias, 2013. "A functional conditional symmetry test for a GARCH-SM model: Power asymptotic properties," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 75-104, March.
    4. Su, Liangjun, 2006. "A simple test for multivariate conditional symmetry," Economics Letters, Elsevier, vol. 93(3), pages 374-378, December.
    5. Xu, Xiuqin & Chen, Ying & Goude, Yannig & Yao, Qiwei, 2021. "Day-ahead probabilistic forecasting for French half-hourly electricity loads and quantiles for curve-to-curve regression," LSE Research Online Documents on Economics 120774, London School of Economics and Political Science, LSE Library.
    6. Taisuke Otsu & Myung Hwan Seo, 2014. "Asymptotics for maximum score method under general conditions," STICERD - Econometrics Paper Series 571, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Di, J. & Kolaczyk, E., 2010. "Complexity-penalized estimation of minimum volume sets for dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1910-1926, October.
    8. Xu, Xiuqin & Chen, Ying & Goude, Yannig & Yao, Qiwei, 2021. "Day-ahead probabilistic forecasting for French half-hourly electricity loads and quantiles for curve-to-curve regression," Applied Energy, Elsevier, vol. 301(C).
    9. 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.
    10. Liangjun Su & Sainan Jin, 2005. "A Bootstrap Test for Conditional Symmetry," Annals of Economics and Finance, Society for AEF, vol. 6(2), pages 251-261, November.
    11. Marcella Niglio, 2007. "Multi-step forecasts from threshold ARMA models using asymmetric loss functions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 395-410, November.
    12. Myung Hwan Seo & Taisuke Otsu, 2016. "Local M-estimation with discontinuous criterion for dependent and limited observations," STICERD - Econometrics Paper Series /589, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    14. Liang, Han-Ying & Liu, Ai-Ai, 2013. "Kernel estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 40-58.
    15. Henderson, Daniel J. & Parmeter, Christopher F., 2015. "A consistent bootstrap procedure for nonparametric symmetry tests," Economics Letters, Elsevier, vol. 131(C), pages 78-82.
    16. 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.
    17. Li, Weiming & Gao, Jing & Li, Kunpeng & Yao, Qiwei, 2016. "Modelling multivariate volatilities via latent common factors," LSE Research Online Documents on Economics 68121, London School of Economics and Political Science, LSE Library.
    18. repec:cep:stiecm:/2014/571 is not listed on IDEAS
    19. Laurent Delsol & Ingrid Van Keilegom, 2020. "Semiparametric M-estimation with non-smooth criterion functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 577-605, April.
    20. Polonik, Wolfgang & Wang, Zailong, 2005. "Estimation of regression contour clusters--an application of the excess mass approach to regression," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 227-249, June.
    21. Polonik, Wolfgang & Yao, Qiwei, 2002. "Set-Indexed Conditional Empirical and Quantile Processes Based on Dependent Data," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 234-255, February.

    More about this item

    Keywords

    Conditional distribution; level set; minimum volume predictor; Nadaraya-Watson estimator; nonlinear time series; predictor; strong mixing.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:ehl:lserod:6311. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.