Identification of Shared Components in Large Ensembles of Time Series Using Dimension Reduction
Ker-Chau Li, Kerby Shedden · Journal of the American Statistical Association · 2002
In this article we present a framework for parsimonious modeling of large ensembles of time series. The idea is to identify a small number of stochastic time series components such that each series in the ensemble is a weighted sum of series-specific realizations of the components. We present an estimation procedure that is computationally tractable for large datasets. Through simulations, we argue that the estimators perform well. We illustrate the method using two datasets: monthly U.S. unemployment rates from 2069 counties over 134 months, and a functional magnetic resonance imaging series covering 10,740 voxels over 108 time points. Our framework is conceptually different from the principal component analysis (PCA) commonly used in multivariate data analysis. We argue that applying PCA directly to an ensemble of time series captures a shared deterministic structure, rather than the series-specific stochastic components that we seek.