On The Limit Distribution Of The Canonical Correlation Coefficients Between The Past And The Future Of A High-Dimensional White Noise
Daria Tieplova, Philippe Loubaton, Leonid Pastur
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04 May 2020
It is shown that the distribution of the estimated canonical correlation coefficients between the past and the future of a high-dimensional multivariate white noise sequence converges almost surely towards a limit distribution whose density is given in closed form. A sketch of proof, based on free probability technics, is provided. Finally, it is briefly explained how this result can be used to produce consistent uncorrelatedness tests in the high-dimensional context.