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Nonparametric estimates for conditional quantiles of time series

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  • Franke, Jürgen
  • Mwita, Peter
  • Wang, Weining

Abstract

We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt, where Xt can ei- ther exogenous variables or lagged variables of Yt . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function, and we prove its asymptotic normality and uni- form strong consistency. The performance of the estimate for light and heavy-tailed distributions of the innovations are 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.

Suggested Citation

  • Franke, Jürgen & Mwita, Peter & Wang, Weining, 2014. "Nonparametric estimates for conditional quantiles of time series," SFB 649 Discussion Papers 2014-012, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2014-012
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    2. 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.
    3. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    4. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    5. Härdle, Wolfgang Karl & Wang, Weining & Yu, Lining, 2016. "TENET: Tail-Event driven NETwork risk," Journal of Econometrics, Elsevier, vol. 192(2), pages 499-513.
    6. Liu, Weiqiang, 2023. "A consistent nonparametric test for the structure change in quantile regression," Economics Letters, Elsevier, vol. 228(C).

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    More about this item

    Keywords

    Conditional quantile; kernel estimate; quantile autoregression; time series; uniform consistency; value-at-risk;
    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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