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Conditional minimum volume predictive regions for stochastic processes

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  • 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
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    File URL: http://eprints.lse.ac.uk/6311/
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    Citations

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    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Henderson, Daniel J. & Parmeter, Christopher F., 2015. "A consistent bootstrap procedure for nonparametric symmetry tests," Economics Letters, Elsevier, vol. 131(C), pages 78-82.
    11. 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.
    12. 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.
    13. repec:cep:stiecm:/2014/571 is not listed on IDEAS
    14. 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.
    15. 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.
    16. Jan G. de Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Tinbergen Institute Discussion Papers 05-068/4, Tinbergen Institute.
    17. 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.
    18. 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).
    19. 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.
    20. 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.
    21. 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.

    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

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