Noise and Financial Stylized Facts: A Stick Balancing Approach
Abstract
:1. Introduction
2. Materials and Methods
- For , there is a critical threshold for (specifically for and for ), below which the sticks quickly falls, thus the point identified by the initial conditions and in phase space results to be unstable, i.e., a repeller. Above the threshold, the system becomes stable, although the equilibrium point may not coincide with the initial one, and spiral trajectories can be observed approaching the node (in this case, of course, the stick never falls). In other words, in correspondence of the critical threshold , there is a sudden transition from a completely disordered regime to a completely ordered one.
- For , a third type of regime appears. Below a different critical threshold (which for becomes ), we always observe a repeller in the phase space, and the sticks always falls; on the other hand, for , the stick never falls, and we again find a spiral node; finally, for , the stick falls again, but we now observe a spiral repeller.
- For we do not find anymore the regime where the initial point is a spiral node. The stick always falls and we pass from finding a repeller to find a spiral repeller in phase space in correspondence of a critical value starting from and increasing as increases. For and for values of , the transition to spiral repeller is no longer observed.
- For values of less than 5, and for less than 4, the stick immediately falls for any initial condition, thus showing repeller behavior. Within the small range , more interesting dynamics start to be observed in the phase space. An example is shown in Figure 1 for and . Finally, for larger values of , the stick still falls but the representative point of the system barely moves from its initial position in the phase space.
- For , the dynamics start to become very sensitive to the noise, for any . Generally, as increases, a spiral-like repelling behavior emerges for values of . Regardless, for and for , a window of complex behavior does appear, with longer trajectories more suitable for allowing statistical analysis.
3. Results
Empirical Data Collection and Comparison with Simulated Data
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Index | First Day | Last Day |
---|---|---|
AEX | 03/01/1983 | 06/07/2022 |
Dow Jones | 04/05/1950 | 06/07/2022 |
Euro stoxx 50 | 31/12/1986 | 06/07/2022 |
FTSE 100 | 30/12/1983 | 06/07/2022 |
FTSE MIB | 31/12/1997 | 06/07/2022 |
France CAC 40 | 09/07/1987 | 06/07/2022 |
IBEX 35 | 05/01/1987 | 06/07/2022 |
Nasdaq | 05/02/1971 | 06/07/2022 |
Nikkei 225 | 03/04/1950 | 06/07/2022 |
S&P 500 | 31/12/1963 | 06/07/2022 |
Asset | First Day | Last Day |
---|---|---|
American Express | 12/12/1972 | 06/07/2022 |
Amazon | 16/05/1997 | 06/07/2022 |
Apple | 15/12/1980 | 06/07/2022 |
BMW | 11/11/1996 | 06/07/2022 |
Colgate | 03/05/1973 | 06/07/2022 |
Ford | 02/06/1972 | 06/07/2022 |
General Electric | 03/01/1962 | 06/07/2022 |
JP Morgan | 18/03/1980 | 06/07/2022 |
Microsoft | 14/03/1986 | 06/07/2022 |
Pfizer | 02/06/1972 | 06/07/2022 |
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Biondo, A.E.; Mazzarino, L.; Pluchino, A. Noise and Financial Stylized Facts: A Stick Balancing Approach. Entropy 2023, 25, 557. https://doi.org/10.3390/e25040557
Biondo AE, Mazzarino L, Pluchino A. Noise and Financial Stylized Facts: A Stick Balancing Approach. Entropy. 2023; 25(4):557. https://doi.org/10.3390/e25040557
Chicago/Turabian StyleBiondo, Alessio Emanuele, Laura Mazzarino, and Alessandro Pluchino. 2023. "Noise and Financial Stylized Facts: A Stick Balancing Approach" Entropy 25, no. 4: 557. https://doi.org/10.3390/e25040557
APA StyleBiondo, A. E., Mazzarino, L., & Pluchino, A. (2023). Noise and Financial Stylized Facts: A Stick Balancing Approach. Entropy, 25(4), 557. https://doi.org/10.3390/e25040557