Nonlinear relative dynamics

Covariance and correlation are two widespread tools in statistics and finance to measure how two entities vary together. Correlation measures the linear relationship between two variables and is not an adequate measure when the two exhibit nonlinear relationships. In this paper, we extend linear correlation to an α-grade monomial one; α values that maximize correlation indicate which type of nonlinear relationship data exhibit. Lagrange representation allows us to define a contro-correlation measure to represent how two entities are not related and a measure of relative variability. Finally, a simulation study and a real-world data application are performed to assess the performance of the proposed methodology.