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Long range financial data and model choice

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  • Davies, Paul Lyndon

Abstract

Long range financial data as typified by the daily returns of the Standard and Poor's index exhibit common features such as heavy tails, long range memory of the absolute values and clustering of periods of high and low volatility. These and other features are often referred to as stylized facts and parametric models for such data are required to reproduce them in some sense. Typically this is done by simulating some data sets under the model and demonstrating that the simulations also exhibits the stylized facts. Nevertheless when the parameters of such models are to be estimated recourse is very often taken to likelihood either in the form of maximum likelihood or Bayes. In this paper we expound a method of determining parameter values which depends solely on the ability of the model to reproduce the relevant features of the data set. We introduce a new measure of the volatility of the volatility and show how it can be combined with the distribution of the returns and the autocorrelation of the absolute returns to determine parameter values. We also give a parametric model for such data and show that it can reproduce the required features.

Suggested Citation

  • Davies, Paul Lyndon, 2006. "Long range financial data and model choice," Technical Reports 2006,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  • Handle: RePEc:zbw:sfb475:200621
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    References listed on IDEAS

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    1. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    2. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    3. Lux, Thomas & Schornstein, Sascha, 2005. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 169-196, February.
    4. F. A. Lutz, 1961. "The Theory of Capital," International Economic Association Series, Palgrave Macmillan, number 978-1-349-08452-4 edited by D. C. Hague, June.
    5. Thomas Lux & Sascha Schornstein, 2002. "Genetic Learning and the Stylized Facts of Foreign Exchange Markets," Computing in Economics and Finance 2002 22, Society for Computational Economics.
    6. Nicholas Kaldor, 1961. "Capital Accumulation and Economic Growth," International Economic Association Series, in: D. C. Hague (ed.), The Theory of Capital, chapter 0, pages 177-222, Palgrave Macmillan.
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    Cited by:

    1. Davies, Laurie & Höhenrieder, Christian & Krämer, Walter, 2012. "Recursive computation of piecewise constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3623-3631.

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