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Innovations in multiple time series analysis
The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large-scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two-step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke (1996). We find that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast and for key variables such as industrial production growth, inflation, and the federal funds rate. The robustness of this finding is confirmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to infinity, which opens the way to using large-scale reduced rank models for empirical analysis. Copyright © 2010 John Wiley & Sons, Ltd.
We discuss methods for modelling multivariate autoregressive time series in terms of a smaller number of index series which
are chosen to provide as complete a summary as possible of the past information contained in the original series necessary
for prediction purposes. The maximum likelihood method of estimation and asymptotic properties of estimators of the coefficients
which determine the index variables, a well as the corresponding autoregressive coefficients, are discussed. A numerical example
is presented to illustrate the use of the autoregressive index models.