Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy?

Abstract

Several economical time series such as exchange rates US$/British Pound, USA Treasure Bonds rates and Warsaw Stock Index WIG have been investigated using the method of recurrence plots. The percentage of recurrence REC and the percentage of determinism DET have been calculated for the original and for shuffled data. We have found that in some cases the values of REC and DET parameters are about 20% lower for the surrogate data which indicates the presence of unstable periodical orbits in the considered data. A similar result has been obtained for the chaotic Lorenz model contaminated by noise. Our investigations suggest that real economical dynamics is a mixture of deterministic and stochastic chaos. We show how a simple chaotic economic model can be controlled by appropriate influence of time-delayed feedback.

Influence of observational noise on the recurrence quantification analysis

“…RQA is based on the distributions of the diagonal, horizontal and vertical lines that are found in the RP. The connection between RPs and RQA forms a powerful tool; both methods have been widely applied in many fields such as physics, medicine, earth science and economics [3,6,7,9,12]. However, the structures that are found in the RPs are not substantiated mathematically.…”

A gradient-based parameter identification method for time-delay chaotic systems

“…Time-delays are present in many real-word chaotic systems, including chemical processes [1], biological systems [2], economic systems [3], and secure communication systems [4]. Sometimes the time-delays appear naturally; sometimes they are deliberately introduced to help stabilize the system or force the system to track real data.…”

Nonlinear dynamics and recurrence plots for detecting financial crisis

“…Although, most applications of this technique has been in physics and biology, it has gained interest in a variety 1 of scientific fields (Marwan et al (2007)). Recurrence plots and recurrence quantification analysis (Zbilut and Webber (1992); ) is gaining some attention in financial studys (Kyrtsou and Vorlow (2005); Strozzi et al (2008); Belaire-Franch (2004); Holyst et al (2001), among others) .This technique is applicable to any time series since it requires no a prior assumptions on the statistical properties, such stationarity, or mathematical structure of the time series. We find this technique as a promising means of analyzing financial data since it is robust against non-stationarity in the data.…”