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Recursive computation of piecewise constant volatilities

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  • Davies, Laurie
  • Höhenrieder, Christian
  • Krämer, Walter

Abstract

Returns of risky assets are often modelled as the product of a volatility function and standard Gaussian white noise. Long range data cannot be adequately approximated by simple parametric models. The choice is between retaining simple models and segmenting the data, or to use a non-parametric approach. There is not always a clear dividing line between the two approaches. In particular, modelling the volatility as a piecewise constant function can be interpreted either as segmentation based on the simple model of constant volatility, or as an approximation to the observed volatility by a simple function. A precise concept of local approximation is introduced and it is shown that the sparsity problem of minimizing the number of intervals of constancy under constraints can be solved using dynamic programming. The method is applied to the daily returns of the German DAX index. In a short simulation study it is shown that the method can accurately estimate the number of breaks for simulated data without prior knowledge of this number.

Suggested Citation

  • Davies, Laurie & Höhenrieder, Christian & Krämer, Walter, 2012. "Recursive computation of piecewise constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3623-3631.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3623-3631
    DOI: 10.1016/j.csda.2010.06.027
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    References listed on IDEAS

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    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. Bernd Wilfling, 2003. "Interest Rate Volatility Prior to Monetary Union under Alternative Pre-Switch Regimes," German Economic Review, Verein für Socialpolitik, vol. 4, pages 433-457, November.
    3. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    4. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    5. José Curto & José Pinto & Gonçalo Tavares, 2009. "Modeling stock markets’ volatility using GARCH models with Normal, Student’s t and stable Paretian distributions," Statistical Papers, Springer, vol. 50(2), pages 311-321, March.
    6. Vassiliou, E. & Demetriou, I.C., 2005. "An adaptive algorithm for least squares piecewise monotonic data fitting," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 591-609, April.
    7. Davies, Paul Lyndon, 2006. "Long range financial data and model choice," Technical Reports 2006,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. repec:spr:alstar:v:101:y:2017:i:3:d:10.1007_s10182-017-0288-1 is not listed on IDEAS
    2. Fried, Roland, 2012. "On the online estimation of local constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3080-3090.
    3. repec:bla:jorssb:v:79:y:2017:i:4:p:1207-1227 is not listed on IDEAS

    More about this item

    Keywords

    Volatility; Stock returns; Heteroskedasticity;

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