Correlation and spectral analysis represent the standard tools to study interdependence
in statistical data. However, for the stochastic processes with heavytailed
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 real data taken
from turbulent plasma of Fusion device and financial market. We conclude that the
codifference serves as a convenient practical tool to study interdependence
forstochastic processes with both infinite and finite variances as well.
