Expected Values in Complex Networks Constructed Using a Compression Algorithm to Time Series

Abstract

This paper introduces a methodology for computing expected values associated with compression networks resulting from the application of compression algorithms to independent and identically distributed random time series. Our analysis establishes a robust correspondence between the calculated expected values and empirically derived results obtained from constructing networks using nondeterministic time series. Notably, the ratio of the average indegree of a network to the computed expected indegree for stochastic time series serves as a versatile metric. It enables the assessment of inherent randomness in time series and facilitates the distinction between nondeterministic and chaotic systems. The metric demonstrates high sensitivity to nondeterminism in both synthetic and real-world datasets, highlighting its capacity to detect subtle disturbances and high-frequency noise, even in series characterized by a deficient sample rate. Our results extend and confirm previous findings in the field.