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Quantile Sieve Estimates For Time Series

Author

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  • Jürgen Franke
  • Jean-Pierre Stockis
  • Joseph Tadjuidje

Abstract

We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t - 1. We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not require the specification of the innovation law. We prove consistency of those estimates and illustrate their good performance for light- and heavy-tailed distributions of the innovations with a small simulation study. As an economic application, we use the estimates for calculating the value at risk of some stock price series.

Suggested Citation

  • Jürgen Franke & Jean-Pierre Stockis & Joseph Tadjuidje, 2007. "Quantile Sieve Estimates For Time Series," SFB 649 Discussion Papers SFB649DP2007-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2007-005
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2007-005.pdf
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    References listed on IDEAS

    as
    1. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
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    4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    5. Franke, Jurgen & Neumann, Michael H. & Stockis, Jean-Pierre, 2004. "Bootstrapping nonparametric estimators of the volatility function," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 189-218.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    8. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Conditional Quantile; Time Series; Sieve Estimate; Neural Network; Qualitative Threshold Model; Uniform Consistency; Value at Risk;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

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