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Estimating Semiparametric ARCH Models by Kernel Smoothing Methods

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  • Enno Mammen
  • Oliver Linton

Abstract

We investigate a class of semiparametric ARCH models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the 'news impact' function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric and nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.

Suggested Citation

  • Enno Mammen & Oliver Linton, 2004. "Estimating Semiparametric ARCH Models by Kernel Smoothing Methods," FMG Discussion Papers dp511, Financial Markets Group.
    • Handle: RePEc:fmg:fmgdps:dp511
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    References listed on IDEAS

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    Cited by:

    1. Perron, Benoit, 2004. "Détection non paramétrique de sauts dans la volatilité des marchés financiers," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 229-251, Juin-Sept.
    2. Srisuma, Sorawoot & Linton, Oliver, 2012. "Semiparametric estimation of Markov decision processes with continuous state space," Journal of Econometrics, Elsevier, vol. 166(2), pages 320-341.
    3. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society.
    4. Linton, Oliver & Mammen, Enno, 2004. "Estimating semiparametric ARCH (∞) models by kernel smoothing methods," LSE Research Online Documents on Economics 24762, London School of Economics and Political Science, LSE Library.

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    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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