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Detecting a structural change in functional time series using local Wilcoxon statistic. (English) Zbl 1432.62303

Summary: Functional data analysis is a part of modern multivariate statistics that analyzes data that provide information regarding curves, surfaces, or anything that varies over a certain continuum. In economics and empirical finance, we often have to deal with time series of functional data, where decision cannot be made easily, for example whether they are to be considered as homogeneous or heterogeneous. A discussion on adequate tests of homogenity for functional data is carried out in literature nowadays. We propose a novel statistic for detecting a structural change in functional time series based on a local Wilcoxon statistic induced by a local depth function proposed by D. Paindaveine and G. Van Bever [J. Am. Stat. Assoc. 108, No. 503, 1105–1119 (2013; Zbl 06224990)], and where a point of the hypothesized structural change is assumed to be known.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G30 Order statistics; empirical distribution functions
62P20 Applications of statistics to economics
62P05 Applications of statistics to actuarial sciences and financial mathematics
62H15 Hypothesis testing in multivariate analysis

Citations:

Zbl 06224990
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References:

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