Forecasting High-Dimensional Time Series via One-Sided Dynamic
Principal Components
Ezequiel Smucler
FCEyN-UBA
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. It is shown that the
ODPC 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 analogues. We
also that prove that asymptotically, when both the number of series and
the sample size go to infinity, if the data follows a dynamic factor
model, the reconstruction obtained with ODPC converges, in mean squared
error, to the common part of the factor model. Monte Carlo results shows
that forecasts obtained by the ODPC compare favorably with other
forecasting methods based on dynamic factor models.