Multiscale characteristics of linear and nonlinear cross-correlations in financial markets

Abstract

With his work "An Inquiry into the Nature and Causes of the Wealth of Nations" published in 1776 [1], the Scottish philosopher and thinker Adam Smith laid foundations for economics as a separate branch of science. In the above-mentioned work, he used the term "invisible hand" meaning a mechanism that directs individual consumers so that their actions are the most beneficial to the whole of society. Although being commonly known and widely covered in the literature, this problem has not been to date put into mathematical formulas in a manner that would enable the market as a whole to be described precisely. This effect is a classic example of an emergent phenomenon, i.e. such a characteristic or property of a system, which has occurred in the system under examination, and which was never previously observed at the level of the individual system components. Phenomena of this type are characteristic of complex systems, where, due to a large number of nonlinear interactions between the elements of the system, evolving structures appear, which cannot be derived from the components in a simple manner. Looking from this perspective on financial markets in a broad sense, one can notice that they perfectly fit into the concept of complex systems. Starting from individual investors in the financial markets or individuals in their households, whose behavior can be described at best in a collective manner, it cannot be determined exactly in which direction the share prices or the domestic economy will, respectively, evolve in the future.