Codifference can detect ergodicity breaking and non-Gaussianity

We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.

• Publication year

  2019

• Venue

  New Journal of Physics

• Publication date

  2019-03-28

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/1367-2630/ab13f3arXiv 1903.11905
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

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