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Unstable volatility functions: the break preserving local linear estimator

Author

Listed:
  • Isabel Casas

    (Aarhus University and CREATES)

  • Irene Gijbels

    (Katholieke Universiteit Leuven)

Abstract

The objective of this paper is to introduce the break preserving local linear (BPLL) estimator for the estimation of unstable volatility functions. Breaks in the structure of the conditional mean and/or the volatility functions are common in Finance. Markov switching models (Hamilton, 1989) and threshold models (Lin and Teräsvirta, 1994) are amongst the most popular models to describe the behaviour of data with structural breaks. The local linear (LL) estimator is not consistent at points where the volatility function has a break and it may even report negative values for finite samples. The estimator presented in this paper generalises the classical LL. The BPLL maintains the desirable properties of the LL with regard to the bias and the boundary estimation, it estimates the breaks consistently and it ensures that the volatility estimates are always positive.

Suggested Citation

  • Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-48
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/09/rp09_48.pdf
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    References listed on IDEAS

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    Cited by:

    1. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    2. Bårdsen Gunnar & Hurn Stanley & McHugh Zöe, 2012. "Asymmetric Unemployment Rate Dynamics in Australia," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(1), pages 1-22, January.
    3. Aslanidis, Nektarios & Casas, Isabel, 2013. "Nonparametric correlation models for portfolio allocation," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2268-2283.
    4. Anders Bredahl Kock & Timo Teräsvirta, 2010. "Forecasting with nonlinear time series models," CREATES Research Papers 2010-01, Department of Economics and Business Economics, Aarhus University.

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    More about this item

    Keywords

    Breaks estimation; Heteroscedasticity; Local linear regression; Nonlinear time series; Volatility estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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