There are many well known and universal properties of the financial time series called stylized fact. One of them states that autocorrelation of increments of the financial time series decays very quickly while the one of their absolute values decays very slowly. The latter property is strongly related to the phenomena of volatility clustering. By using high frequency empirical data we state that The foundation of this type of behavior is indeed the long-term autocorrelation of inter-event times. Such dependence can be described in terms of the stochastic model based on Continuous-Time Random Walk [1], the model introduced by physicists Montroll and Weiss nearly 50 years ago [2]. The model with dependent inter-event times can significantly contribute to successful description of high-frequency financial data by CTRW [3,4].

[1] E. W. Montroll, G. H. Weiss, J. Math. Phys, 6(2):167181, 1965.
[2] R. Kutner, J. Masoliver, arXiv:1612.02221v1 (2016)
[3] T. Gubiec, R. Kutner, Phys. Rev. E 82, 046119 (2010)
[4] T. Gubiec, R. Kutner, arXiv:1305.6797v3 (2016)

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/32840 must be provided.

1. Is Implied Volatility based mostly on recent price activity?
2. Coevolving complex networks in the model of social interaction
3. Modeling Endogenous Contagion on O/N Interbank Market
4. Continuous-time random walk with memory in study of autocorrelations present in financial time series
5. Statistical mechanics of coevolving Ising model
6. Intraday correlation structure for high frequency financial data
7. Analysis of times between events by methods of statistical physics
8. Fractional Market Model and its Verification on the Warsaw Stock Exchange
9. Bose-Einstein condensation shown by Monte Carlo simulation
10. Remarks on the possible universal mechanism of the non-linear long-term autocorrelations in financial time-series
11. Random walk on a linear chain with a quenched distribution of jump lengths
12. Modified Fermi-Dirac Statistics of Fermionic Lattice Gas by the Back-Jump Correlations
13. Thermal neutron scattering from the hydrogen-metal systems in terms of general multi-sublattice jump diffusion model - II: Remarks on hydrogen diffusion in the α-phase of Nb-H
14. Simple molecular mechanisms of heat transfer: Debye relaxation versus power-law
15. Stock market context of the Lévy walks with varying velocity
16. Tracer diffusion on two coupled lines: The long-time tail of the velocity autocorrelation function compared to the mode-coupling prediction
17. Distribution for Fermionic Discrete Lattice Gas within the Canonical Ensemble
18. Monte Carlo Simulations of Lattice Gases Exhibiting Quantum Statistical Distributions
19. Modeling of super-extreme events: An application to the hierarchical Weierstrass-Mandelbrot Continuous-time Random Walk
20. Biased random walk on a biased random walk
21. Possible origin of the non-linear long-term autocorrelations within the Gaussian regime
22. Applications of statistical mechanics to non-brownian random motion
23. Real-time numerical simulation of the Carnot cycle
24. Quantum statistics and discreteness. Differences between the canonical and grand canonical ensembles for a fermionic lattice gas
25. Tracer diffusion in honey-comb lattice correlations over several consecutive jumps
26. Spatio–temporal coupling in the continuous-time Lévy flights
27. Determination of the chemical diffusion coefficient by Monte Carlo simulation of the center-of-mass propagation
28. Tracer Diffusion in Concentrated Lattice Gas Models. Rectangular Lattices with Anisotropic Jump Rates
29. Study of the non-linear autocorrelations within the Gaussian regime
30. Anomalous transport and diffusion versus extreme value theory
31. Diffusion in concentrated lattice gases: Intermediate incoherent dynamical scattering function for tagged particles on a square lattice
32. Modeling of income distribution in the European Union with the Fokker-Planck equation
33. Susceptibility and transport coefficient in a transient state on a one-dimensional lattice. I. Extended linear response and diffusion
34. Report on Foundation and Organization of Econophysics Graduate Courses at Faculty of Physics of University of Warsaw and Department of Physics and Astronomy of the Wrocław University
35. Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach
36. Higher-order analysis within Weierstrass hierarchical walks
37. Correlated hopping in honeycomb lattice: tracer diffusion coefficient at arbitrary lattice gas concentration
38. Diffusion in one-dimensional bosonic lattice gas
39. Structural and topological phase transitions on the German Stock Exchange 
40. Hierarchical spatio-temporal coupling in fractional wanderings. (I) Continuous-time Weierstrass flights
41. Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model—I: Theory
42. Random walk on a random walk
43. Diffusion in concentrated lattice gases. VI. Tracer diffusion on two coupled linear chains
44. Comparative Analysis of Income Distributions in the European Union and the United States
45. Excess Noise for Driven Diffusive Systems
46. Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice
47. Chemical diffusion in the lattice gas of non-interacting particles
48. Diffusion in concentrated lattice gases. Self-diffusion of noninteracting particles in three-dimensional lattices
49. Diffusion in concentrated lattice gases. II. Particles with attractive nearest-neighbor interaction on three-dimensional lattices
50. Anomalous Diffusion: From Basics to Applications
51. Mean square displacement of a tracer particle in a hard-core lattice gas
52. Diffusion in concentrated lattice gases IV. Diffusion coefficient of tracer particle with different jump rate
53. Diffusion in concentrated lattice gases. V. Particles with repulsive nearest-neighbor interaction on the face-centered-cubic lattice
54. Stochastic simulations of time series within Weierstrass–Mandelbrot walks
55. Income distribution in the European Union versus in the United States
56. Universality of market superstatistics
57. Study of time series reversibility with Pomeau criterion
58. Physics of polish banking system
59. Dynamic bifurcations on financial markets
60. Coevolution in model of social interactions: getting closer to real-world networks
61. Income and wealth distribution of Norwegian households
62. Higher-order phase transitions on financial markets
63. Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution
64. Backward jump continuous-time random walk: An application to market trading
65. Universality of market superstatistics. Superscaling
66. Rozmowa o Ekonofizycje - Akademickie Radio Kampus
67. Modeling of large claims in a non-life insurance company
68. Correlations and dependencies in high-frequency stock market data
69. Continuous-Time Random Walk models with memory. An application to description of market dynamics
70. Superextreme Events and Their Impact on Characteristics of Time Series
71. The role of driving parameters of the three-state Ising model on the stability of the reconstruction of financial market phenomena
72. Analysis of leptokurtosis in model distributions and simulated noises
73. Application of the MST technique to the analysis of cross-correlations in the Warsaw Stock Exchang.
74. Modelling of annual European Union household incomes by using an equilibrium solution of the threshold Fokker-Planck equation
75. Catastrophic bifurcations on financial markets
76. Asymmetric noises on a stock exchange.
77. Influence of super-extreme events on a Weierstrass-Mandelbrot Continuous-Time Random Walk
78. Non-Gaussian statistics on the Forex
79. Backward jump Continuous-Time Random Walk on a stock market. What is the true origin of the autocorrelation on the market?
80. Study of  households' income  in Poland and European Union by using the statistical physics approach
81. The non-gaussian continuous-time random walk analisys of the option dynamics
82. Share price movements as non-independent continuous-time random walk
83. Problem of rare events in modelling of the financial state of insurance company
84. Study of households' income in Poland by using the statistical physics approach
85. News from application of the Mittag-Leffler function to house and financial markets
86. Anomalous left-sided multifractal structure of intertransation time-intervals and the possible third-order phase transition on financial market
87. Model of the fractional viscoelastic market
88. Multifractality within the continuous-time random walk in financial markets
89. Fractional Market Model and its verification on stock markets of small size
90. Econophysics on Faculty of Physics at Warsaw University
91. Dynamics of the Warsaw Stock Exchange index as analysed by the fractional relaxation equation
92. Non-linear long-term autocorrelations present in empirical and synthetic high-frequency financial time-series. Possibility of risk classification