Abstract
Cross-approximate entropy(XApEn)quantifies the mutual orderliness of simultaneously recorded time series. Despite being derived from the firmly established solitary entropies, it has never reached their reputation and deployment. The aim of this study is to identify the problems that preclude widerXApEnimplementation and to develop a set of solutions. Exact expressions forXApEnand its constitutive parts are derived and compared to values estimated from artificial data. This comparison revealed vast regions within the parameter space that do not guarantee reliable probability estimation, makingXApEnestimates inconsistent. A simple correction to one of theXApEnprocedural steps is proposed. Three sets of formulae for joint parameter selection are derived. The first one is intended to maximize threshold profile. The remaining ones minimizeXApEninstability according to the strong and weak criteria. The derived expressions are verified using cardiovascular signals recorded from rats (long signals) and healthy volunteers (short clinical signals), proposing a change of traditional parameter guidelines.
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