Asymptotically consistent estimation of the number of change points in highly dependent time series

Azadeh Khaleghi 1 Daniil Ryabko 1
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : The problem of change point estimation is considered in a general framework where the data are generated by arbitrary unknown stationary ergodic process distributions. This means that the data may have long-range dependencies of an arbitrary form. In this context the consistent estimation of the number of change points is provably impossible. A formulation is proposed which overcomes this obstacle: it is possible to find the correct number of change points at the expense of introducing the additional constraint that the correct number of process distributions that generate the data is provided. This additional parameter has a natural interpretation in many real-world applications. It turns out that in this formulation change point estimation can be reduced to time series clustering. Based on this reduction, an algorithm is proposed that finds the number of change points and locates the changes. This algorithm is shown to be asymptotically consistent. The theoretical results are complemented with empirical evaluations.
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Conference papers
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https://hal.inria.fr/hal-01026583
Contributor : Daniil Ryabko <>
Submitted on : Monday, July 21, 2014 - 6:36:58 PM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM

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  • HAL Id : hal-01026583, version 1

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Azadeh Khaleghi, Daniil Ryabko. Asymptotically consistent estimation of the number of change points in highly dependent time series. International Conference on Machine Learning (ICML), Jun 2014, Beijing, China. pp.539-547. ⟨hal-01026583⟩

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