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Adaptive Detection of Multiple Change-Points in Asset Price Volatility

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Long Memory in Economics

Summary

This chapter considers the multiple change-point problem for time series, including strongly dependent processes, with an unknown number of change-points. We propose an adaptive method for finding the segmentation, i.e., the sequence of change-points τ with the optimal level of resolution. This optimal segmentation \( \hat \tau \) is obtained by minimizing a penalized contrast function J(τ, y)+ßpen(τ). For a given contrast function J(τ, y) and a given penalty function pen(τ), the adaptive procedure for automatically choosing the penalization parameter β is such that the segmentation \( \hat \tau \) does not strongly depend on β. This algorithm is applied to the problem of detection of change-points in the volatility of financial time series, and compared with Vostrikova’s (1981) binary segmentation procedure.

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Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques, Université René Descartes and Université Paris-Sud, Paris

    Marc Lavielle

  2. Laboratoire de Statistique Appliquée et MOdélisation Stochastique (SAMOS), Université Paris 1, Paris

    Gilles Teyssière

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  1. Marc Lavielle
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  2. Gilles Teyssière
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Editors and Affiliations

  1. Laboratoire de Statistique Appliquée et de Modélisation Stochastique (SAMOS), Panthéon Sorbonne, Centre Pierre Mendès, Université Paris 1, 90 rue de Tolbiac, 75634, Paris Cedex 13, France

    Gilles Teyssière

  2. L’Ecole des Hautes Etudes en Sciences Sociales (EHESS), Université Aix-Marseille III, 2 rue de la Charité, 13002, Marseille, France

    Alan P. Kirman

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Lavielle, M., Teyssière, G. (2007). Adaptive Detection of Multiple Change-Points in Asset Price Volatility. In: Teyssière, G., Kirman, A.P. (eds) Long Memory in Economics. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34625-8_5

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