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Unstable volatility functions: the break preserving local linear estimator

  • Isabel Casas

    ()

    (Aarhus University and CREATES)

  • Irene Gijbels

    (Katholieke Universiteit Leuven)

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.

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File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_48.pdf
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-48.

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Length: 25
Date of creation: 22 Oct 2009
Date of revision:
Handle: RePEc:aah:create:2009-48
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Valerie Cerra & Sweta Chaman Saxena, 2003. "Did Output Recover From the Asian Crisis?," IMF Working Papers 03/48, International Monetary Fund.
  2. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
  3. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA.
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  5. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(2), pages 235-272, June.
  6. Ziegelmann, Flavio A., 2002. "Nonparametric Estimation Of Volatility Functions: The Local Exponential Estimator," Econometric Theory, Cambridge University Press, vol. 18(04), pages 985-991, August.
  7. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
  8. Cai, Zongwu, 2001. "Weighted Nadaraya-Watson regression estimation," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 307-318, February.
  9. Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
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