Pattern formation in time series systems due to viscoelastic behavior: Case studies in uniform distribution, normal distribution, stock market index, and music

Güngör Gündüz ()
Additional contact information
Güngör Gündüz: Kimya Mühendisliği Bölümü, Orta Doğu Teknik Üniversitesi, Ankara 06800, Turkey

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 09, 1-41

Abstract: A new methodology was introduced to investigate the pattern formation in time series systems due to their viscoelastic behavior. Four stochastic processes, uniform distribution, normal distribution, Nasdaq-100 stock market index, and a melody were studied within this context. The time series data were converted into vectorial forms in a scattering diagram. The sequential vectors can be split into its in-line (or conservative) and out-of-line (or dissipative) components. Thus, one can define the storage and loss modulus for conservative, and dissipative components, respectively. Instead of using the geometric Brownian equation which involves Wiener noise term, the changes were taken into consideration at every step by introducing “lethargy” concept and the deviation from it. Thus, the mathematics is somehow simplified, and the dynamical behavior of time series systems can be elucidated at every step of change. The viscoelastic behavior of time series systems reveals patterns of the viscoelastic parameters such as storage and loss modulus, and also of thermodynamic work-like and heat-like properties. Besides, there occur some minima and maxima in the distribution of the angles between the sequential vectors in the scattering diagram. The same is true for the change of entropy of the system.

Keywords: Pattern formation; scattering diagram; viscoelasticity; thermodynamics; fluctuation; Wiener; lethargy; bifurcation; branching; entropy; curvature (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183118500857
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:29:y:2018:i:09:n:s0129183118500857

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183118500857

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().