Properties of balanced flows with bottlenecks: Common stylized facts in finance and vibration-driven vehicles

We study experimentally the properties of the flow of mechanical vibration-driven vehicles confined in two chambers connected through a narrow opening. We report that the density of particles around the opening presents critical behavior and scaling properties. By mapping this density to the financial market price, we document that the main stylized facts observed in financial systems have their counterparts in the mechanical system. The experimental model accurately reproduces financial properties such as scaling of the price fluctuation, volatility clustering, and multiscaling.

Figure 1

(a) Snapshots of the VDV system. In panel B the distance $d_3$ is depicted. (b) Density time series of vibration-driven vehicles where A and B indicate the particular configurations shown in (a). (c) Time evolution of the polarization parameter $P_{\kappa }$. (d) Probability density function of $P_{\kappa }$.

Figure 2

Autocorrelation function of the (a) VDV and (b) BTCUSD returns (red solid line), absolute returns (royal blue short-dashed line), square returns (green long-dash–short-dashed line), and logarithm of absolute returns (navy blue long-dash–double-short-dashed line).

Figure 3

Autocorrelation function of the absolute (blue short-dashed line) and squared returns (green long-dash–short-dashed line) for the (a) VDV and (b) BTCUSD systems. Black solid lines stand for PL fits. Also shown is the first lag of the autocorrelation for different exponents $\alpha$ for the (c) VDV and (d) BTCUSD systems.

Figure 4

Power-law exponents and coefficient of determination obtained from fits of the autocorrelation of the absolute values of density when estimated at different measurement points.

Figure 5

Complementary cumulative distribution function for the standardized absolute returns of the (a) VDV and (b) BTCUSD systems computed at different time steps $j$. The solid line stands for the CCDF of the nearest Gaussian distribution.

Figure 6

Probability of zero return as a function of time step $j$ for the (a) VDV and (b) BTCUSD systems. The exponents of the power-law fits are $\delta =0.81$ for the VDV system and $\delta =0.59$ for BTCUSD system.

Figure 7

(a) Plot of $K_q\left(j\right)$ of $R_{\rho }$ as a function of time step $j$ for $q=1$, 2, 3, and 4. Solid lines show the PL fits. (b) Plot of $K_q\left(j\right)$ and PL fits for the BTCUSD system. (c) Exponents $qQ\left(q\right)$ as a function of $q$ for the VDV system, showing a nonlinear relationship. (d) The $qQ\left(q\right)$ function for the BTCUSD system.

Figure 8

Detrended fluctuation analysis for the (a) VDV and (b) BTCUSD systems. Solid lines stand for PL fits.

Figure 9

Comparison between the PDF of $P_{\kappa }$ for $\kappa =[2,4]$.

Figure 10

(a) Decay of the autocorrelation of $|R_{\rho }|$ as a function of $\kappa$. (b) Coefficient of determination obtained from the fitting procedure.

Figure 11

(a) Complementary cumulative distribution function for the VDV returns. The solid line stands for SE fit. (b) The CCDF for BTCUSD returns and the corresponding PL fit shown by the solid line.