3 research outputs found
Quantum Bohmian-inspired potential to model non–Gaussian time series and Its application in financial markets
We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case
Quantum Bohmian Inspired Potential to Model Non-Gaussian Events and the Application in Financial Markets
We have implemented quantum modeling mainly based on Bohmian Mechanics to
study time series that contain strong coupling between their events. We firstly
propose how compared to normal densities, our target time series seem to be
associated with a higher number of rare events, and Gaussian statistics tend to
underestimate these events' frequency drastically. To this end, we suggest that
by imposing Gaussian densities to the natural processes, one will seriously
neglect the existence of extreme events in many circumstances. The central
question of our study concerns the consideration of the effects of these rare
events in the corresponding probability densities and studying their role from
the point of view of quantum measurements. To model the non-Gaussian behavior
of these time-series, we utilize the multifractal random walk (MRW) approach
and control the non-Gaussianity parameter accordingly. Using the
framework of quantum mechanics, we then examine the role of in
quantum potentials derived for these time series. Our Bohmian quantum analysis
shows that the derived potential takes some negative values in high frequencies
(its mean values), then substantially increases, and the value drops again for
the rare events. We thus conclude that these events could generate a potential
barrier that the system, lingering in a non-Gaussian high-frequency region,
encounters, and their role becomes more prominent when it comes to transversing
this barrier. In this study, as an example of the application of quantum
potential outside of the micro-world, we compute the quantum potentials for the
S\&P financial market time series to verify the presence of rare events in the
non-Gaussian densities for this real data and remark the deviation from the
Gaussian case.Comment: 7 pages, 2 figure
Coupled Criticality Analysis of Inflation and Unemployment.
In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish “regular” from “rare” events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the “multifractal random wall” model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the “bivariate multifractal random walk” that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables’ increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises