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Abstract:
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In this work I will present a new statistical test for determining if a panel of functional time series is separable. Separability is property which can dramatically improve statistical efficiency while substantially reducing model complexity. In this context, separability means that the covariance structure factors into the produce of two functions, one depending only on time and the other depending only on the coordinates of the panel. Separability is especially useful for functional data as it means that functional principal components are the same for each member of the panel. However, in practice, such a strong assumption must be checked. Our test is based on functional norm differences and provides a very stable and powerful test. Our methodology will be illustrated via simulations and a financial application. Asymptotic theory will also be discussed.
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