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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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    Cited by:

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    2. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    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. Liu, Weiqiang, 2023. "A consistent nonparametric test for the structure change in quantile regression," Economics Letters, Elsevier, vol. 228(C).
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    6. 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.

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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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