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Unstable volatility: the break-preserving local linear estimator

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  • Isabel Casas
  • Irene Gijbels

Abstract

The objective of this paper is to introduce the break-preserving local linear (BPLL) estimator for the estimation of unstable volatility functions for independent and asymptotically independent processes. Breaks in the structure of the conditional mean and/or the volatility functions are common in Finance. Nonparametric estimators are well suited for these events due to the flexibility of their functional form and their good asymptotic properties. However, the local polynomial kernel estimators are not consistent at points where the volatility function has a break. The estimator presented in this paper generalises the classical local linear (LL). The BPLL estimator maintains the desirable properties of the LL estimator with regard to the bias and the boundary estimation while it estimates the breaks consistently. An extensive Monte Carlo study is shown as well as detailed proofs of the estimator asymptotic behaviour.

Suggested Citation

  • Isabel Casas & Irene Gijbels, 2012. "Unstable volatility: the break-preserving local linear estimator," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 883-904, December.
  • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:883-904
    DOI: 10.1080/10485252.2012.720981
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    File URL: http://hdl.handle.net/10.1080/10485252.2012.720981
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    References listed on IDEAS

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    1. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
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    Cited by:

    1. Cizek, Pavel & Koo, Chao, 2017. "Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series," Discussion Paper 2017-017, Tilburg University, Center for Economic Research.
    2. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    3. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.

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