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Title: Testing separability of functional time series Authors:  Panayiotis Constantinou - The Pennsylvania State University (United States) [presenting]
Piotr Kokoszka - Colorado State University (USA)
Matthew Reimherr - Pennsylvania State University (United States)
Abstract: A significance test is derived and studied for determining if a panel of functional time series is separable. In this context, separability means that the covariance structure factors into the product of two functions, one depending only on time and the other depending only on the coordinates of the panel. Separability is a property which can dramatically improve computational efficiency by substantially reducing model complexity. It is especially useful for functional data as it implies that the functional principal components are the same for each member of the panel. However such an assumption must be verified before proceeding with further inference. Our approach is based on functional norm differences and provides a test with well controlled size and high power. In addition to an asymptotic justification, our methodology is validated by a simulation study. It is applied to functional panels of particulate pollution and stock market data.