Chaos in historical prices and volatilities with five-dimensional euclidean spaces

Alves, P.R.L.

doi:10.1016/j.csfx.2019.100002

Cited by 10 publications

(10 citation statements)

References 28 publications

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“…Chaos is a seemingly irregular and complex phenomenon that exists in the real world. Therefore, the emergence of chaos may be an important condition to verify whether the model is consistent with reality [53]. The Lyapunov exponent spectrum and bifurcation diagram are used to prove the appearance of chaos.…”

Section: Dynamic Analysis Of Gddsmentioning

confidence: 99%

Impact of environmental tax on green development: A nonlinear dynamical system analysis

Fan

Yin

2019

PLoS ONE

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With green development becoming a global movement, environmental tax has been adopted by many governments to promote green development. This study analyzes the impact of environmental tax on green development by using a four-dimension dynamical system. The establishment of the system is based on the complex and dynamic interactions among economic development, pollution emissions, resources consumption, and environmental tax, where roles of environmental tax are reflected by the linear parameters. A theoretic analysis shows the complexity of the behavior of the system. Mainly, the existence of chaos is inferred by Lyapunov exponent spectrum and bifurcation diagram, then verified by the presence of a chaotic attractor. An empirical study of the green development dynamical system in China demonstrates the particular evolution paths of economic growth, pollution intensity, and resource intensity under different environmental tax parameters. Results indicate a robust beneficial role of environmental tax on green development. Furthermore, when an environmental tax is imposed, a firm government control, an active consumer awareness, an advanced technology level can stimulate economic growth, decrease pollution intensity, and control the resource intensity. But the government control has a stronger effect. This study provides a viable and promising approach to analyze the role of imposing an environmental tax on green development and may have potential application in other areas and countries.

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Section: Dynamic Analysis Of Gddsmentioning

confidence: 99%

Impact of environmental tax on green development: A nonlinear dynamical system analysis

Fan

Yin

2019

PLoS ONE

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“…The approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ) are alternative tools for time series analysis for capturing nonlinear dynamics. In addition, scholars applied these entropies to several fields in econophysics [ 32 , 33 , 34 , 35 , 36 ] and financial phenomena [ 37 , 38 , 39 , 40 , 41 , 42 ]. Therefore, in this paper, we apply these three metrics to the price sequence of the cryptocurrency market for investigating the evolutionary unpredictability or complexity.…”

Section: Introductionmentioning

confidence: 99%

The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market

Kim

Lee

2021

Entropy

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The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis.

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“…With a little use of traditional statistical methods, we aim to investigate the impact of the novel coronavirus disease (COVID-19) on the financial markets worldwide using the driven iterated function system approach, which uses the concept of fractals and chaos game. Fractals have widely been used for the study of financial markets (Alves, 2019 ; Bianchi & Frezza, 2017 ; Kristoufek, 2013 ; Lux, 1998 ) but with complex methodologies. We use a simple and widely used concept of chaos game representation (CGR) of DNA sequences (Jeffrey, 1990 ; Almeida et al, 2001 ; Randhawa et al, 2020 , Pratibha et al 2020 ) and modify the CGR method to accommodate the financial data.…”

Section: Introductionmentioning

confidence: 99%

A Study of the International Stock Market Behavior During COVID-19 Pandemic Using a Driven Iterated Function System

et al. 2021

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We propose a novel approach to visualize and compare financial markets across the globe using chaos game representation (CGR) of iterated function systems (IFS). We modified a fractal method, widely used in life sciences, and applied it to study the effect of COVID-19 on global financial markets. This modified driven IFS approach is used to generate compact fractal portraits of the financial markets in form of percentage CGR (PC) plots and subtraction percentage (SP) plots. The markets over different periods are compared and the difference is quantified through a parameter called the proximity (Pr) index. The reaction of the financial market across the globe and volatility to the current pandemic of COVID-19 is studied and modeled successfully. The imminent bearish and a surprise bullish pattern of the financial markets across the world is revealed by this fractal method and provides a new tool to study financial markets.

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Chaos in historical prices and volatilities with five-dimensional euclidean spaces

Cited by 10 publications

References 28 publications

Impact of environmental tax on green development: A nonlinear dynamical system analysis

Impact of environmental tax on green development: A nonlinear dynamical system analysis

The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market

A Study of the International Stock Market Behavior During COVID-19 Pandemic Using a Driven Iterated Function System

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