Forecasting Multiple Time Series With One-Sided Dynamic Principal Components

Autores
Peña, Daniel; Smucler, Ezequiel; Yohai, Victor Jaime
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models.
Fil: Peña, Daniel. Universidad Carlos III de Madrid. Instituto de Salud; España
Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
DIMENSIONALITY REDUCTION
DYNAMIC FACTOR MODELS
HIGH-DIMENSIONAL TIME SERIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/92383
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Forecasting Multiple Time Series With One-Sided Dynamic Principal ComponentsPeña, DanielSmucler, EzequielYohai, Victor JaimeDIMENSIONALITY REDUCTIONDYNAMIC FACTOR MODELSHIGH-DIMENSIONAL TIME SERIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models.Fil: Peña, Daniel. Universidad Carlos III de Madrid. Instituto de Salud; EspañaFil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAmerican Statistical Association2019-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/92383Peña, Daniel; Smucler, Ezequiel; Yohai, Victor Jaime; Forecasting Multiple Time Series With One-Sided Dynamic Principal Components; American Statistical Association; Journal of The American Statistical Association; 2-2019; 1-430162-1459CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/01621459.2018.1520117info:eu-repo/semantics/altIdentifier/doi/10.1080/01621459.2018.1520117info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:10:13Zoai:ri.conicet.gov.ar:11336/92383instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:10:13.802CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
title Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
spellingShingle Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
Peña, Daniel
DIMENSIONALITY REDUCTION
DYNAMIC FACTOR MODELS
HIGH-DIMENSIONAL TIME SERIES
title_short Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
title_full Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
title_fullStr Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
title_full_unstemmed Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
title_sort Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
dc.creator.none.fl_str_mv Peña, Daniel
Smucler, Ezequiel
Yohai, Victor Jaime
author Peña, Daniel
author_facet Peña, Daniel
Smucler, Ezequiel
Yohai, Victor Jaime
author_role author
author2 Smucler, Ezequiel
Yohai, Victor Jaime
author2_role author
author
dc.subject.none.fl_str_mv DIMENSIONALITY REDUCTION
DYNAMIC FACTOR MODELS
HIGH-DIMENSIONAL TIME SERIES
topic DIMENSIONALITY REDUCTION
DYNAMIC FACTOR MODELS
HIGH-DIMENSIONAL TIME SERIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models.
Fil: Peña, Daniel. Universidad Carlos III de Madrid. Instituto de Salud; España
Fil: Smucler, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Yohai, Victor Jaime. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting high-dimensional multiple time series. An alternating least-squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogs. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follow a dynamic factor model, the reconstruction obtained with ODPC converges in mean square to the common part of the factor model. The results of a simulation study show that the forecasts obtained with ODPC compare favorably with those obtained using other forecasting methods based on dynamic factor models.
publishDate 2019
dc.date.none.fl_str_mv 2019-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/92383
Peña, Daniel; Smucler, Ezequiel; Yohai, Victor Jaime; Forecasting Multiple Time Series With One-Sided Dynamic Principal Components; American Statistical Association; Journal of The American Statistical Association; 2-2019; 1-43
0162-1459
CONICET Digital
CONICET
url http://hdl.handle.net/11336/92383
identifier_str_mv Peña, Daniel; Smucler, Ezequiel; Yohai, Victor Jaime; Forecasting Multiple Time Series With One-Sided Dynamic Principal Components; American Statistical Association; Journal of The American Statistical Association; 2-2019; 1-43
0162-1459
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/01621459.2018.1520117
info:eu-repo/semantics/altIdentifier/doi/10.1080/01621459.2018.1520117
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Statistical Association
publisher.none.fl_str_mv American Statistical Association
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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