  Correlation and spectral analysis represent the standard tools to study
interdependence in statistical data. However, for the stochastic processes with
heavy-tailed distributions such that the variance diverges, these tools are
inadequate. The heavy-tailed processes are ubiquitous in nature and finance. We
here discuss codifference as a convenient measure to study statistical
interdependence, and we aim to give a short introductory review of its
properties. By taking different known stochastic processes as generic examples,
we present explicit formulas for their codifferences. We show that for the
Gaussian processes codifference is equivalent to covariance. For processes with
finite variance these two measures behave similarly with time. For the
processes with infinite variance the covariance does not exist, however, the
codifference is relevant. We demonstrate the practical importance of the
codifference by extracting this function from simulated as well as from real
experimental data. We conclude that the codifference serves as a convenient
practical tool to study interdependence for stochastic processes with both
infinite and finite variances as well.
