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Smooth principal components for investigating changes in covariances over time


Address for correspondence: Claire Miller, School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW, UK.


Summary.  The complex interrelated nature of multivariate systems can result in relationships and covariance structures that change over time. Smooth principal components analysis is proposed as a means of investigating whether and how the covariance structure of multiple response variables changes over time, after removing a smooth function for the mean, and this is motivated and illustrated by using data from an aircraft technology study and a lake ecosystem. Inferential procedures are investigated in the cases of independent and dependent errors, with a bootstrapping procedure proposed to detect changes in the direction or variance of components.