Department of Mathematics

Indian Institute Of Technology Madras , Chennai
  • Mathematics Department Shifted to NAC Office of the Department of Mathematics is moved from HSB to New Academic Complex (NAC) 5th and 6th Floor

Codifference as a practical tool to measure interdependence

Speaker : Prof. hab. inz. Agnieszka Wylomanska (Wroclaw University of Technology, Poland)


Abstract :

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.

Key Speaker Prof. hab. inz. Agnieszka Wylomanska (Wroclaw University of Technology, Poland)
Place NAC 522
Start Time 3:00 PM
Finish Time 4:00 PM
External Link None