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Abstract:

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.

Registro:

Documento: Artículo
Título:Forecasting Multiple Time Series With One-Sided Dynamic Principal Components
Autor:Peña, D.; Smucler, E.; Yohai, V.J.
Filiación:Department of Statistics and Institute of Financial Big Data, Universidad Carlos III de Madrid, Getafe, Spain
Department of Mathematics and Statistics, Universidad Torcuato Di Tella, Buenos Aires, Argentina
Department of Mathematics, Instituto de Calculo, Universidad de Buenos Aires, Buenos Aires, Argentina
School of Exact and Natural Sciences, Universidad de Buenos Aires, Argentina
CONICET, Buenos Aires, Argentina
Palabras clave:Dimensionality reduction; Dynamic factor models; High-dimensional time series
Año:2019
DOI: http://dx.doi.org/10.1080/01621459.2018.1520117
Título revista:Journal of the American Statistical Association
Título revista abreviado:J. Am. Stat. Assoc.
ISSN:01621459
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v_n_p_Pena

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Citas:

---------- APA ----------
Peña, D., Smucler, E. & Yohai, V.J. (2019) . Forecasting Multiple Time Series With One-Sided Dynamic Principal Components. Journal of the American Statistical Association.
http://dx.doi.org/10.1080/01621459.2018.1520117
---------- CHICAGO ----------
Peña, D., Smucler, E., Yohai, V.J. "Forecasting Multiple Time Series With One-Sided Dynamic Principal Components" . Journal of the American Statistical Association (2019).
http://dx.doi.org/10.1080/01621459.2018.1520117
---------- MLA ----------
Peña, D., Smucler, E., Yohai, V.J. "Forecasting Multiple Time Series With One-Sided Dynamic Principal Components" . Journal of the American Statistical Association, 2019.
http://dx.doi.org/10.1080/01621459.2018.1520117
---------- VANCOUVER ----------
Peña, D., Smucler, E., Yohai, V.J. Forecasting Multiple Time Series With One-Sided Dynamic Principal Components. J. Am. Stat. Assoc. 2019.
http://dx.doi.org/10.1080/01621459.2018.1520117