Strong laws for recurrence quantification analysis
Marian Grend\'ar, Jana Majerov\'a, Vladim\'ir \v{S}pitalsk\'y
TL;DR
This paper establishes strong laws of large numbers for recurrence rate and determinism in recurrence quantification analysis, linking these measures to correlation sums and providing rigorous statistical foundations.
Contribution
It introduces a novel theoretical framework connecting recurrence measures to correlation sums and proves strong laws of large numbers for these measures.
Findings
Recurrence rate and determinism are expressed via correlation sums.
Strong laws of large numbers are proved for these measures.
Provides rigorous statistical foundations for recurrence quantification analysis.
Abstract
The recurrence rate and determinism are two of the basic complexity measures studied in the recurrence quantification analysis. In this paper, the recurrence rate and determinism are expressed in terms of the correlation sums, and strong laws of large numbers are given for them.
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