Generalized Dynamic principal components are presented and it is shown how to define one side inear combinations of the present and past values of the series that minimize the reconstruction mean squared error (ODPC). It is shown that the ODPC introduced in this paper 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 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 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.
Daniel Peña holds Master in Engineering and Ph.D. degrees from Universidad Politécnica de Madrid, Sociology and Statistics Degrees from Universidad Complutense de Madrid and ITP Business Administration, Harvard University. He was Founding Director of the Department of Statistics and of Institute UC3M-BS in Financial Big Data and President (Rector) of Universidad Carlos III de Madrid (UC3M), where is now Professor. He has supervised more than 30 Ph.D. thesis, published 14 books and more than 220 research articles on Time Series, Robust and Diagnostics methods, Multivariate Analysis, Bayesian Statistics and Econometrics with application to Social Science, Economics and Engineering. His research has received several awards, as the 2006 Youden Prize for the best paper in Technometrics, the 2011 Jaime I Prize in Economics, the 2011 Award Engineer of the Year by the Colegio Oficial de Ingenieros Industriales, Madrid, and the 2010 Lifetime Career Award, Alumni ETSII-UPM. He is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, the Royal Statistical Society, elected member of the International Statistical Institute and member of the Royal Academy of Sciences in Spain.
Light refreshments will be served around 15:45.