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Non-parametric Estimation of GARCH (2, 2) Volatility model: A new Algorithm

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  • Cassim, Lucius

Abstract

The main objective of this paper is to provide an estimation approach for non-parametric GARCH (2, 2) volatility model. Specifically the paper, by combining the aspects of multivariate adaptive regression splines(MARS) model estimation algorithm proposed by Chung (2012) and an algorithm proposed by Buhlman and McNeil(200), develops an algorithm for non-parametrically estimating GARCH (2,2) volatility model. Just like the MARS algorithm, the algorithm that is developed in this paper takes a logarithmic transformation as a preliminary analysis to examine a nonparametric volatility model. The algorithm however differs from the MARS algorithm by assuming that the innovations are i.d.d. The algorithm developed follows similar steps to that of Buhlman and McNeil (200) but starts by semi parametric estimation of the GARCH model and not parametric while relaxing the dependency assumption of the innovations to avoid exposing the estimation procedure to risk of inconsistency in the event of misspecification errors.

Suggested Citation

  • Cassim, Lucius, 2018. "Non-parametric Estimation of GARCH (2, 2) Volatility model: A new Algorithm," MPRA Paper 86861, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:86861
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    File URL: https://mpra.ub.uni-muenchen.de/86861/1/MPRA_paper_86861.pdf
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    References listed on IDEAS

    as
    1. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    2. 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.
    3. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    6. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    7. 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.
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    More about this item

    Keywords

    GARCH (2; 2); MARS; Algorithm; Parametric; Semi parametric; Nonparametric;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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