Predictive information and distance between past and future of a time series

Umberto Triacca

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 16, 8230-8235

Abstract: A characterization for the nullity of the cosine angle between two subspaces of a Hilbert space is established. Given a time series x, we use this characterization in order to investigate the relationship between the notions of predictor space and distance between the information contained in the past and in the future of x. In particular, we prove that the predictor space of x coincides with the zero vector space {0} if and only if this distance achieves its maximum value.

Date: 2017
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DOI: 10.1080/03610926.2016.1177081

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