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Estimating semiparametric ARCH (∞) models by kernel smoothing methods

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  • Linton, Oliver
  • Mammen, Enno

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 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 daily returns. We find some evidence of asymmetric news impact functions in the data.

Suggested Citation

  • Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (∞) models by kernel smoothing methods," LSE Research Online Documents on Economics 58068, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:58068
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    More about this item

    Keywords

    ARCH; inverse problem; kernel estimation; news impact curve; nonparametric regression; profile likelihood; semiparametric estimation; volatility;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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