Abstract
This chapter is devoted to the problems of time-series clustering and change-point analysis. Clustering is grouping together samples generated by the same distributions, while change-point problems are concerned with delimiting parts of a sample that are generated by a different process distributions. Building on the results of the previous chapter, here we are trying to solve these more general problems avoiding the need to answer the “same-different” question about process distributions (discrimination), and only using the asymptotically consistent distance estimates that we have. It turns out that this is enough to solve the clustering problem when the number of clusters is known, as well as several versions of the changepoint problem, without the need to make any assumptions beyond stationarity and ergodicity. In particular, the means, variances, or even single-dimensional marginals of all the processes in question may be the same. For the change-point problem, the main focus of this chapter is on the case of a single change; on overview of the more general formulations is given, with the corresponding results presented without proofs.
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Ryabko, D. (2019). Clustering and Change-Point Problems. In: Asymptotic Nonparametric Statistical Analysis of Stationary Time Series. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-12564-6_4
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DOI: https://doi.org/10.1007/978-3-030-12564-6_4
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