In this paper, we investigate the causality in sense of Granger for functional time series. The concept series is defined, and a statistical procedure testing hypothesis non-causality proposed. based on projections dynamic principal components use multivariate test. A comparative study with existing procedures shows good results our An illustration real dataset provided to attest performance pr...

We study a class of separable sample covariance matrices the form Q˜1:=A˜1/2XB˜X∗A˜1/2. Here, A˜ and B˜ are positive definite whose spectrums consist bulk plus several spikes, that is, larger eigenvalues separated from bulks. Conceptually, we call Q˜1 spiked matrix model. On one hand, this model includes as special case with B˜=I. other it allows for more general correlations datasets. In parti...