Empirical Dynamic Quantiles for Visualization of High-Dimensional Time Series Article Swipe
Daniel Peña
,
Ruey S. Tsay
,
Ruben H. Zamar
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.6084/m9.figshare.7701638
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.6084/m9.figshare.7701638
The empirical quantiles of independent data provide a good summary of the underlying distribution of the observations. For high-dimensional time series defined in two dimensions, such as in space and time, one can define empirical quantiles of all observations at a given time point, but such time-wise quantiles can only reflect properties of the data at that time point. They often fail to capture the dynamic dependence of the data. In this article, we propose a new definition of empirical dynamic quantiles (EDQ) for high-dimensional time series that mitigates this limitation by imposing that the quantile must be one of the observed time series. The word dynamic emphasizes the fact that these newly defined quantiles capture the time evolution of the data. We prove that the EDQ converge to the time-wise quantiles under some weak conditions as the dimension increases. A fast algorithm to compute the dynamic quantiles is presented and the resulting quantiles are used to produce summary plots for a collection of many time series. We illustrate with two real datasets that the time-wise and dynamic quantiles convey different and complementary information. We also briefly compare the visualization provided by EDQ with that obtained by functional depth. The R code and a vignette for computing and plotting EDQ are available athttps://github.com/dpena157/HDts/.
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https://openalex.org/W4394383271Canonical identifier for this work in OpenAlex
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https://doi.org/10.6084/m9.figshare.7701638Digital Object Identifier
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Empirical Dynamic Quantiles for Visualization of High-Dimensional Time SeriesWork title
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datasetOpenAlex work type
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enPrimary language
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2019Year of publication
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2019-01-01Full publication date if available
- Authors
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Daniel Peña, Ruey S. Tsay, Ruben H. ZamarList of authors in order
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https://doi.org/10.6084/m9.figshare.7701638Publisher landing page
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.6084/m9.figshare.7701638Direct OA link when available
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Quantile, Series (stratigraphy), Visualization, Computer science, Time series, Computer graphics (images), Data mining, Econometrics, Mathematics, Geology, Machine learning, PaleontologyTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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