Abstract
In this paper, we investigate the causality in the sense of Granger for functional time series. The concept of causality for functional time series is defined, and a statistical procedure of testing the hypothesis of non-causality is proposed. The procedure is based on projections on dynamic functional principal components and the use of a multivariate Granger test. A comparative study with existing procedures shows the good results of our test. An illustration on a real dataset is provided to attest the performance of the proposed procedure.
Highlights
We provide a new testing procedure based on dynamic functional principal components
We define the operator of covariance Γ Z of the stationary functional time series Zt by: Γ Z (U ) = E[h Z, U i Z ], ∀U ∈ H, (1)
Hörmann et al [17] have proposed a dynamic version of functional principal component analysis (FPCA) that is more efficient for functional time series than the traditional
Summary
The classical notion of causality in the sense of Granger (see [5]) has been extended to the functional time series cases. This extension is important and useful to the statistical community. We recall the notion of causality for functional stationary time series and propose tests of non-causality. We studied another procedure that does not use the functional nature of the data, which is called the classical test. This procedure is based on differentiating the time series and using a multivariate Granger test.
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