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Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods

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  • O. Linton
  • E. Mammen

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 part and the 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. Copyright The Econometric Society 2005.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 3 (05)
Pages: 771-836

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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:3:p:771-836

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Cited by:
  1. Gregory Connor & Oliver Linton & Matthias Hagmann, 2007. "Efficient Estimation of a Semiparametric Characteristic-Based Factor Model of Security Returns," FMG Discussion Papers dp599, Financial Markets Group.
  2. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, 02.
  3. Oliver Linton & Enno Mammen, 2006. "Nonparametric transformation to white noise," LSE Research Online Documents on Economics 4426, London School of Economics and Political Science, LSE Library.
  4. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
  5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  6. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.

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