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Nonparametric estimates for conditional quantiles of time series

Author

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  • Jürgen Franke
  • Peter Mwita
  • Weining Wang

Abstract

We consider the problem of estimating the conditional quantile of a time series $$\{ Y_t\}$$ { Y t } at time $$t$$ t given covariates $$\varvec{X}_{t}$$ X t , where $$\varvec{X}_{t}$$ X t can be either exogenous variables or lagged variables of $${ Y_t}$$ Y t . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function, and we prove its asymptotic normality and uniform strong consistency. The performance of the estimate for light and heavy-tailed distributions of the innovations is evaluated by a simulation study. Finally, the technique is applied to estimate VaR of stocks in DAX, and its performance is compared with the existing standard methods using backtesting. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Jürgen Franke & Peter Mwita & Weining Wang, 2015. "Nonparametric estimates for conditional quantiles of time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 107-130, January.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:1:p:107-130
    DOI: 10.1007/s10182-014-0234-4
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    1. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    2. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    3. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
    4. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    5. Horváth, Lajos & Yandell, Brian S., 1988. "Asymptotics of conditional empirical processes," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 184-206, August.
    6. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    7. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    8. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    9. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(1), pages 46-68, March.
    12. Boente, G. & Fraiman, R., 1995. "Asymptotic Distribution of Smoothers Based on Local Means and Local Medians under Dependence," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 77-90, July.
    13. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    14. Abberger, Klaus, 1994. "Nichtparametrische Schätzung bedingter Quantile in Finanzmarktdaten," Discussion Papers, Series II 225, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    15. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
    16. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    17. Rama Krishnaiah, Y. S., 1990. "On the Glivenko-Cantelli theorem for generalized empirical processes based on strong mixing sequences," Statistics & Probability Letters, Elsevier, vol. 10(5), pages 439-447, October.
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    Cited by:

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    3. Härdle, Wolfgang Karl & Wang, Weining & Yu, Lining, 2016. "TENET: Tail-Event driven NETwork risk," Journal of Econometrics, Elsevier, vol. 192(2), pages 499-513.
    4. Takashi Miyazaki, 2019. "Clarifying the Response of Gold Return to Financial Indicators: An Empirical Comparative Analysis Using Ordinary Least Squares, Robust and Quantile Regressions," JRFM, MDPI, vol. 12(1), pages 1-18, February.
    5. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
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    More about this item

    Keywords

    Kernel estimate; Quantile autoregression; Uniform consistency; Value at Risk (VaR);
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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