Does Chaos Matter in Financial Time Series Analysis?

Abstract

The apparent randomness of financial market led some economists to approach chaos theory as a theoretical framework able to explain those fluctuations. This interest is because some nonlinear deterministic systems with few degrees of freedom create signals that mimic stochastic signals from the point of view of traditional time series analysis but with a deepener analysis performed by adequate tools could be chaotic. The aim of this paper is explorative in its nature, pointing to investigate chaos literature in order to grasp the difficulties typical of these applied researches and to see if something new is happening.

Financial markets’ deterministic aspects modeled by a low-dimensional equation

“…Given this situation, we are happy to show that a substantial contribution of determinism is found in the data 4 , 79 . For forecasting, the latter is sufficient; the question whether the whole of the data should be termed chaotic or stochastic is, seen in this perspective, of a more ’academic’ nature 1 , 63 , where the contradicting arguments available may indicate a lack of appropriate technical or theoretical descriptors to deal with such type of data.…”

“…Substantial mathematically minded economic research has dealt with the question whether financial data contain in a substantial manner low-dimensional chaotic features, or whether their nature requires the stochastic approach predominantly used by the practitioners dealing with the analysis of financial markets. A comprehensive survey of the various methods that have been used, and the conclusions they have arrived at, has recently been published 1 . In that survey and more generally, the approaches advocating a chaotic nature of the data have almost exclusively relied on indirect statistical quantifiers, such as evaluation of Lyapunov exponents and fractal dimensions 2 , 3 , data recurrence quantification analysis 4 , or BDS-testing 5 .…”

On risk and market sentiments driving financial share price dynamics

“…Regarding the vexed question of the presence of chaos in finance and economics, Faggini et al [16], while conducting a comprehensive review of the subject, affirm that "no natural deterministic explanation can justify the observed financial fluctuations produced by external shocks or by inherent randomness". On the other hand, theoretical and empirical studies bring to light numerous shreds of evidence about chaos and determinism in real-world data.…”

Bursts and Regularization in Financial Markets: Deterministic or Stochastic?

“…where MAE (1) is the mean absolute error of the model of interest and MAE (2) is the error of some benchmark model 31 . A value greater than unity indicates that the chosen model performs worse than the benchmark.…”

“…For an overview of the methods used and conclusions drawn from a potentially mild bias towards chaos in economics see Ref. 1 . To present, the made conclusions were almost exclusively based on indirect, mostly averaged, statistical time series quantifiers, such as Lyapunov exponents, fractal dimensions 2 , recurrence quantification analysis 3 or BDS testing 4 .…”