Daniel Peña, Department of Statistics and Institute of Financial Big Data, Universidad Carlos III de Madrid, Spain
Date: 14 MAY 2019 at 14:30
Event location: Aula 22, 2° floor, Piazza Scaravilli, Bologna
Type: Statistics Seminars
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. Usu-
ally dynamic principal components have been defined as functions
of past and future values of the series and therefore they are not ap-
propriate for forecasting purposes. On the contrary, it is shown that
the ODPC introduced in this paper can be successfully used for fore-
casting 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 analogues. We also prove that asymp-
totically, when both the number of series and the sample size go to
infinity, if the data follows a dynamic factor model, the reconstruc-
tion 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 favourably with those
obtained using other forecasting methods based on dynamic factor
models.
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