Forecasting Multiple Time Series With One-Sided Dynamic Principal Components

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...

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Detalles Bibliográficos
Autores principales:	Peña, D., Smucler, E., Yohai, V.J.
Formato:	JOUR
Materias:	Dimensionality reduction Dynamic factor models High-dimensional time series
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_01621459_v_n_p_Pena
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_01621459_v_n_p_Pena
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spelling	todo:paper_01621459_v_n_p_Pena2023-10-03T15:01:35Z Forecasting Multiple Time Series With One-Sided Dynamic Principal Components Peña, D. Smucler, E. Yohai, V.J. Dimensionality reduction Dynamic factor models High-dimensional time series 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. Supplementary materials for this article are available online. © 2019, © 2019 American Statistical Association. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01621459_v_n_p_Pena
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Dimensionality reduction Dynamic factor models High-dimensional time series
spellingShingle	Dimensionality reduction Dynamic factor models High-dimensional time series Peña, D. Smucler, E. Yohai, V.J. Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
topic_facet	Dimensionality reduction Dynamic factor models High-dimensional time series
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. Supplementary materials for this article are available online. © 2019, © 2019 American Statistical Association.
format	JOUR
author	Peña, D. Smucler, E. Yohai, V.J.
author_facet	Peña, D. Smucler, E. Yohai, V.J.
author_sort	Peña, D.
title	Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
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
url	http://hdl.handle.net/20.500.12110/paper_01621459_v_n_p_Pena
work_keys_str_mv	AT penad forecastingmultipletimeserieswithonesideddynamicprincipalcomponents AT smuclere forecastingmultipletimeserieswithonesideddynamicprincipalcomponents AT yohaivj forecastingmultipletimeserieswithonesideddynamicprincipalcomponents
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Forecasting Multiple Time Series With One-Sided Dynamic Principal Components

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