Chaoticity versus stochasticity in financial markets: Are daily S&amp;P 500 return dynamics chaotic?

Vogl, Markus; Rötzel, Peter

doi:10.1016/j.cnsns.2021.106218

Cited by 22 publications

(52 citation statements)

References 108 publications

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“…Before elaborating on the analysis framework itself, it is relevant to reconcile the contribution and relevance of the propagated inherent paradigm shift in quantitative modeling, namely, the previous determination of the empirical DGP and its Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series… DOI: http://dx.doi.org/10.5772/intechopen.106213 characteristics before selecting referring mathematical procedures and models [40,44]. Referring back to the introductory mentioned expected market increase by around 20 Bn.…”

Section: Framework Overviewmentioning

confidence: 99%

“…The former statement is an allegory for the vast dilemma concerning the determination of the true, mostly unknown nature of complex dynamical (real-world) systems -whether it be stochasticity or chaoticity [40]. These systems are almost graphically similar and cannot be differentiated by respective statistical standard tests [29,41].…”

Section: Introductionmentioning

confidence: 99%

“…To solve this ongoing debate, Vogl and Rötzel [40] and Vogl [44] successfully proposed distinct analysis frameworks, enabling the clear and safe quantification and determination of the underlying (empirical) DGPs of time-series data sets. Nonetheless, due to publication technical reasons, Vogl and Rötzel [40] present a framework specification tailored toward solely stationary time-series, while Vogl [44] supposes additional customization for non-stationary data. However, these specifications originate from one original, singular and holistic chaos analysis framework for nonlinear time-series, which will be presented in its totality hereinafters.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, since the determination of the (empirical) DGP by the proposed framework is by far trivial in its application, owing to a large variety of advanced algorithms to be implemented, this chapter is purposed to provide a clear and distinct practical guideline on how to successfully implement the denoted analysis framework. Particularly, the determination of 'scaling regions' via correlation sum and correlation dimensional schemes (refer to [45][46][47]) and the reconstruction algorithms of (strange, fractal) attractors of complex dynamical systems with chaotic traits (see [10,48]) represent one of the main emphases, among others, since many erroneous conductions are possible and are widely dispersed throughout the scientific literature [25,40,45]. The distinct goal and aim of this chapter are to provide the researcher and practitioner with an empirical-practical guide on how to implement the presented chaos analysis framework successfully, thus, determining the (empirical) DGP and reconstructing potentially existing system attractors out of a scalar timeseries given [40,44].…”

Section: Introductionmentioning

confidence: 99%

“…Particularly, the determination of 'scaling regions' via correlation sum and correlation dimensional schemes (refer to [45][46][47]) and the reconstruction algorithms of (strange, fractal) attractors of complex dynamical systems with chaotic traits (see [10,48]) represent one of the main emphases, among others, since many erroneous conductions are possible and are widely dispersed throughout the scientific literature [25,40,45]. The distinct goal and aim of this chapter are to provide the researcher and practitioner with an empirical-practical guide on how to implement the presented chaos analysis framework successfully, thus, determining the (empirical) DGP and reconstructing potentially existing system attractors out of a scalar timeseries given [40,44]. Moreover, the insights provided are mostly independent of the framework, generalizable and abstractable to any other kind of subsequent or related empirical analyses conducted.…”

Section: Introductionmentioning

confidence: 99%

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Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Vogl¹

2023

Nonlinear Systems - Recent Developments and Advances

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Within this chapter, a practical introduction to a nonlinear analysis framework tailored for time-series data is provided, enabling the safe quantification of underlying evolutionary dynamics, which describe the referring empirical data generating process. Furthermore, its application provides the possibility to distinct between underlying chaotic versus stochastic dynamics. In addition, an optional combination with (strange) attractor reconstruction algorithms to visualize the denoted system’s dynamics is possible. Since the framework builds upon a large variety of algorithms and methods, its application is by far trivial, especially, in hindsight of reconstruction algorithms for (strange) attractors. Therefore, a general implementation and application guideline for the correct algorithm specifications and avoidance of pitfalls or other unfavorable settings is proposed and respective (graphical) empirical examples are shown. It is intended to provide the readers the possibility to incorporate the proposed analysis framework themselves and to conduct the analyses and reconstructions properly with correct specifications and to be knowledgeable about misleading propositions or parameter choices. Finally, concluding remarks, future avenues of research and future refinements of the framework are proposed.

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Section: Framework Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Vogl¹

2023

Nonlinear Systems - Recent Developments and Advances

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Assessing stock market contagion and complex dynamic risk spillovers during COVID-19 pandemic

Xiao²,

Zheng³

2023

Nonlinear Dyn

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A very important area where COVID-19 has seriously disrupted is the global financial markets, where stock markets have experienced great turmoil. To shed light on the nature of this turmoil and to characterize nonlinear dynamics in inter-market risk transmission, we formally test the existence of inter-stock market contagion, identify the main channel once the presence of contagion has been established, and assess the upside and downside risk spillovers dynamically focusing on complexity during pre-COVID-19 and post-COVID-19 periods. Applying multiple measures including time-varying conditional value-at-risk based on copula theory, and sample entropy methods, considering a sample covering seven countries (USA, UK, France, Germany, Japan, Brazil, China) during the period from 4 January 2019 to 30 December 2020, we show that contagion is widely present among analysed stock markets with only a few exceptions and that “portfolio rebalancing” as opposed to “wealth constraint” occurs more as the main channel of transmission. All market pairings exhibit significant bilateral upside and downside spillovers after the outbreak of COVID-19. A significant shift in complexity of risk spillover dynamics is evident for most recipient countries following the shock of COVID-19, among which all but China display a downward shift. The findings of this paper could help regulators, politicians, and portfolio risk managers amid the uncertainty created by the COVID-19 pandemic.

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Recurrence-based reconstruction of dynamic pricing attractors

Oberst

2023

Nonlinear Dyn

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Dynamic pricing depends on the understanding of uncertain demand. We ask the question whether a stochastic system is sufficient to model this uncertainty. We propose a novel paradigm based on statistical analysis of recurrence quantification measures. The paradigm fits nonlinear dynamics by simultaneously optimizing both the determinism and the trapping time in recurrence plots and identifies an optimal time delay embedding. We firstly apply the paradigm on well-known deterministic and stochastic systems including Duffing systems and multi-fractional Gaussian noise. We then apply the paradigm to optimize the sampling of empirical point process data from RideAustin, a company providing ride share service in the city of Austin, Texas, the USA, thus reconstructing a period-7 attractor. Results show that in deterministic systems, an optimal embedding exists under which recurrence plots exhibit robust diagonal or vertical lines. However, in stochastic systems, an optimal embedding often does not exist, evidenced by the inability to shrink the standard deviation of either the determinism or the trapping time. By means of surrogate testing, we also show that a Poisson process or a stochastic system with periodic trend is insufficient to model uncertainty contained in empirical data. By contrast, the period-7 attractor dominates and well models nonlinear dynamics of empirical data via irregularly switching of the slow and the fast dynamics. Findings highlight the importance of fitting and recreating nonlinear dynamics of data in modeling practical problems.

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Chaoticity versus stochasticity in financial markets: Are daily S&P 500 return dynamics chaotic?

Cited by 22 publications

References 108 publications

Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Chaos Analysis Framework: How to Safely Identify and Quantify Time-Series Dynamics

Assessing stock market contagion and complex dynamic risk spillovers during COVID-19 pandemic

Recurrence-based reconstruction of dynamic pricing attractors

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