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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Bibliographic Details
Published in:Journal of the American Statistical Association 2019-10, Vol.114 (528), p.1683-1694
Main Authors: Peña, Daniel, Smucler, Ezequiel, Yohai, Victor J.
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Convergence
Dimensionality reduction
Dynamic factor models
Forecasting
High-dimensional time series
Mathematical models
Reconstruction
Regression analysis
Simulation
Statistical methods
Statistics
Time series
Values
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Summary: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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2018.1520117