Polarization of forecast densities: A new approach to time series classification

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Time series classification has been extensively explored in many fields of study. Most methods are based on the historical or current information extracted from data. However, if interest is in a specific future time period, methods that directly relate to forecasts of time series are much more appropriate. An approach to time series classification is proposed based on a polarization measure of forecast densities of time series. By fitting autoregressive models, forecast replicates of each time series are obtained via the biascorrected bootstrap, and a stationarity correction is considered when necessary. Kernel estimators are then employed to approximate forecast densities, and discrepancies of forecast densities of pairs of time series are estimated by a polarization measure, which evaluates the extent to which two densities overlap. Following the distributional properties of the polarization measure, a discriminant rule and a clustering method are proposed to conduct the supervised and unsupervised classification, respectively. The proposed methodology is applied to both simulated and real data sets, and the results show desirable properties.
Original languageEnglish
Pages (from-to)345 - 361
Number of pages17
JournalComputational Statistics and Data Analysis
Volume70
DOIs
Publication statusPublished - 2014

Cite this

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title = "Polarization of forecast densities: A new approach to time series classification",
abstract = "Time series classification has been extensively explored in many fields of study. Most methods are based on the historical or current information extracted from data. However, if interest is in a specific future time period, methods that directly relate to forecasts of time series are much more appropriate. An approach to time series classification is proposed based on a polarization measure of forecast densities of time series. By fitting autoregressive models, forecast replicates of each time series are obtained via the biascorrected bootstrap, and a stationarity correction is considered when necessary. Kernel estimators are then employed to approximate forecast densities, and discrepancies of forecast densities of pairs of time series are estimated by a polarization measure, which evaluates the extent to which two densities overlap. Following the distributional properties of the polarization measure, a discriminant rule and a clustering method are proposed to conduct the supervised and unsupervised classification, respectively. The proposed methodology is applied to both simulated and real data sets, and the results show desirable properties.",
author = "Shen Liu and Maharaj, {Elizabeth Ann} and Inder, {Brett Andrew}",
year = "2014",
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pages = "345 -- 361",
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Polarization of forecast densities: A new approach to time series classification. / Liu, Shen; Maharaj, Elizabeth Ann; Inder, Brett Andrew.

In: Computational Statistics and Data Analysis, Vol. 70, 2014, p. 345 - 361.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Polarization of forecast densities: A new approach to time series classification

AU - Liu, Shen

AU - Maharaj, Elizabeth Ann

AU - Inder, Brett Andrew

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Y1 - 2014

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AB - Time series classification has been extensively explored in many fields of study. Most methods are based on the historical or current information extracted from data. However, if interest is in a specific future time period, methods that directly relate to forecasts of time series are much more appropriate. An approach to time series classification is proposed based on a polarization measure of forecast densities of time series. By fitting autoregressive models, forecast replicates of each time series are obtained via the biascorrected bootstrap, and a stationarity correction is considered when necessary. Kernel estimators are then employed to approximate forecast densities, and discrepancies of forecast densities of pairs of time series are estimated by a polarization measure, which evaluates the extent to which two densities overlap. Following the distributional properties of the polarization measure, a discriminant rule and a clustering method are proposed to conduct the supervised and unsupervised classification, respectively. The proposed methodology is applied to both simulated and real data sets, and the results show desirable properties.

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