Econophysics Forum
https://www3.unifr.ch/econophysics
enOrder flow in the financial markets from the perspective of the Fractional L\'{e}vy stable motion
https://www3.unifr.ch/econophysics/?q=content/order-flow-financial-markets-perspective-fractional-levy-stable-motion
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It is a challenging task to identify the best possible models</pre><pre>
based on given empirical data of real stochastic time series. Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big challenge for researchers. The widely used long-range memory and self-similarity estimators give varying values of the parameters as these estimators themselves are developed for the specific models of time series. Here we investigate the order disbalance time series constructed from the limit order book data of the financial markets under fractional L\'{e}vy stable motion assumption. Our results suggest that previous findings of persistence in order flow are related to the power-law distribution of order sizes. Still, orders have stable estimates of anti-correlation for the 18 randomly selected stocks, when Absolute value and Higuchi's estimators are implemented. The burst duration analysis based on the first passage problem of time series and implemented in this research gives different estimates of the Hurst parameter more consistent with the uncorrelated increment cases.</pre></div></div></div>Thu, 06 May 2021 13:51:10 +0000Gontis28037 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/order-flow-financial-markets-perspective-fractional-levy-stable-motion#commentsStrategically positioning cooperators can facilitate the contagion of cooperation
https://www3.unifr.ch/econophysics/?q=content/strategically-positioning-cooperators-can-facilitate-contagion-cooperation
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<p>The spreading of cooperation in structured population is a challenging problem which can be observed at different scales of social and biological organization. Generally, the problem is studied by evaluating the chances that few initial invading cooperators, randomly appearing in a network, can lead to the spreading of cooperation. In this paper we demonstrate that in many scenarios some cooperators are more influential than others and their initial positions can facilitate the spreading of cooperation. We investigate six different ways to add initial cooperators in a network of cheaters, based on different network-based measurements. Our research reveals that strategically positioning the initial cooperators in a population of cheaters allows to decrease the number of initial cooperators necessary to successfully seed cooperation. The strategic positioning of initial cooperators can also help to shorten the time necessary for the restoration of cooperation. The optimal ways in which the initial cooperators should be placed is, however, non-trivial in that it depends on the degree of competition, the underlying game, and the network structure. Overall, our results show that, in structured populations, few cooperators, well positioned in strategically chosen places, can spread cooperation faster and easier than a large number of cooperators that are placed badly.</p>
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</div></div></div>Thu, 14 Jan 2021 14:42:04 +0000mcavaliere28036 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/strategically-positioning-cooperators-can-facilitate-contagion-cooperation#commentsOn Forecasts of the COVID-19 Pandemic
https://www3.unifr.ch/econophysics/?q=content/forecasts-covid-19-pandemic
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The current COVID-19 pandemic creates seemingly chaotic devastations. Scientists worldwide have failed to predict actual outcomes. A comprehensive study by (Ioannidis, et.al. 2020) examines detailed reasons for the failures. A second study (Taleb, et.al 2020) questions the approaches used for pandemic prediction. They find that the pandemic distribution has a fat tail, and proclaim this result has significant implication for pandemic predictions. The latter study used the Generalized Pareto Distribution. This study examines the historical pandemic series using the truncated Pareto I distribution. It uses the least-squares-fit estimate for this distribution to determine a precise estimate of the tail exponent 1.15. This study uses Monte Carlo techniques to generate synthetic power law series with this exponent. Applying extreme value theory, it compares the characteristics of the pandemic series to that of power law synthetics. The comparisons show excellent agreement between the historical pandemic series and the synthetic ones. This shows that the pandemic’s distribution behaves like the synthetics with this power law, confirming that this distribution is likely to have a fat tail. This study then examines the worldwide countries’ mortality rates in ways similar to those used for the historical pandemic. It finds that this distribution may also have a fat tail with exponent 1.45. This work notes that the historical pandemic distribution is fixed, while it shows that the distribution of the mortality rates continually evolves. The pandemic and mortality distributions’ power law behaviors red-light their high danger, demanding extreme caution for dealing with plagues. However, the fat-tailed distributions cannot make specific predictions. Improved forecasts like those championed by (Ioannidis, et.al. 2020) may provide useful guidance for and aid in monitoring the worldwide countries’ individual pandemic responses.</p>
</div></div></div>Wed, 11 Nov 2020 20:32:25 +0000t.j.mazurek28035 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/forecasts-covid-19-pandemic#commentsModel of continuous random cascade processes in financial markets
https://www3.unifr.ch/econophysics/?q=content/model-continuous-random-cascade-processes-financial-markets
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively combines with volatility; the other does so additively. Assuming that the latter acts perturbatively on the system, then the model parameters are estimated by application to an actual stock price time series. Numerical calculation of the Fokker--Planck equation derived from the stochastic differential equation is conducted using the estimated values of parameters. The results reproduce the pdf of the empirical volatility, the multifractality of the time series, and other empirical facts.</p>
</div></div></div>Tue, 27 Oct 2020 08:25:19 +0000jmaskawa28034 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/model-continuous-random-cascade-processes-financial-markets#commentsAn Elementary Humanomics Approach to Boundedly Rational Quadratic Models
https://www3.unifr.ch/econophysics/?q=content/elementary-humanomics-approach-boundedly-rational-quadratic-models
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>We take a refreshing new look at boundedly rational quadratic models in economics using some elementary modeling of the principles put forward in the book Humanomics by Vernon L. Smith and Bart J. Wilson. A simple model is introduced built on the fundamental Humanomics principles of gratitude/resentment felt and the corresponding action responses of reward/punishment in the form of higher/lower payoff transfers. There are two timescales: one for strictly self-interested action, as in economic equilibrium, and another governed by feelings of gratitude/resentment. One of three timescale scenarios is investigated: one where gratitude/resentment changes much more slowly than economic equilibrium ("quenched model"). Another model, in which economic equilibrium occurs over a much slower time than gratitude/resent evolution ("annealed" model) is set up, but not investigated. The quenched model with homogeneous interactions turns out to be a non-frustrated spin-glass model. A two-agent quenched model with heterogeneous aligning (ferromagnetic) interactions is analyzed and yields new insights into the critical quenched probability p (1 − p) that represents the empirical frequency of opportunity for agent i to take action for the benefit (hurt) of other that invokes mutual gratitude (resentment). A critical quenched probability p*_i , i = 1, 2, exists for each agent. When p < p*_i , agent i will choose action in their self-interest. When p > p*_i , agent i will take action sensitive to their interpersonal feelings of gratitude/resentment and thus reward/punish the initiating benefit/hurt. We find that the p*_i are greater than one-half, which implies agents are averse to resentful behavior and punishment. This was not built into the model, but is a result of its properties, and consistent with Axiom 4 in Humanomics about the asymmetry of gratitude and resentment. Furthermore, the agent who receives less payoff is more averse to resentful behavior; i.e., has a higher critical quenched probability. For this particular model, the Nash equilibrium has no predictive power of Humanomics properties since the rewards are the same for self-interested behavior, resentful behavior, and gratitude behavior. Accordingly, we see that the boundedly rational Gibbs equilibrium does indeed lead to richer properties.</p>
</div></div></div>Wed, 26 Aug 2020 20:29:55 +0000mjcampbell28033 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/elementary-humanomics-approach-boundedly-rational-quadratic-models#commentsBoundedly-Rational Fast-Tuning Control Theory and Statistical Mechanics
https://www3.unifr.ch/econophysics/?q=content/boundedly-rational-fast-tuning-control-theory-and-statistical-mechanics
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>We construct a model of control theory with 'fast-tuning' of parameters relative to the ambient dynamics of the system. The parameters are tuned 'myopically' (i.e., small changes are made), along with a random perturbation that allows for a large net change with certain probability. This is modeled using a drift-diffusion stochastic partial differential equation. The idea is to model 'bounded rationality' of the agent(s) tuning the parameters-that is, they may not follow the optimal path for tuning because of a lack of complete information about the system, errors in judgement, and/or a desire to experiment and test other options.</p>
</div></div></div>Wed, 26 Aug 2020 20:27:44 +0000mjcampbell28032 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/boundedly-rational-fast-tuning-control-theory-and-statistical-mechanics#commentsSpurious memory in non-equilibrium stochastic models of imitative behavior
https://www3.unifr.ch/econophysics/?q=content/spurious-memory-non-equilibrium-stochastic-models-imitative-behavior
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent 3/2 of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents.</p>
</div></div></div>Thu, 04 Jun 2020 07:39:12 +0000Gontis28031 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/spurious-memory-non-equilibrium-stochastic-models-imitative-behavior#commentsThe consentaneous model of the financial markets exhibiting spurious nature of long-range memory
https://www3.unifr.ch/econophysics/?q=content/consentaneous-model-financial-markets-exhibiting-spurious-nature-long-range-memory
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contribution we investigate burst and inter-burst duration statistics of volatility in the financial markets employing the consentaneous model. Our analysis provides an evidence that empirical statistical properties of burst and inter-burst duration can be explained by non-linear stochastic differential equations driving the volatility in the financial markets. This serves as an strong argument that long-range memory in finance can have spurious nature.</p>
</div></div></div>Thu, 04 Jun 2020 07:33:48 +0000Gontis28030 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/consentaneous-model-financial-markets-exhibiting-spurious-nature-long-range-memory#commentsBessel-like birth-death process
https://www3.unifr.ch/econophysics/?q=content/bessel-birth-death-process
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize the Bessel-like birth-death process having clear representation by the SDEs. The new process helps to integrate the alternatives of description and to derive the equations for the probability density function (PDF) of the burst and inter-burst duration of the proposed continuous time birth-death processes.</p>
</div></div></div>Thu, 04 Jun 2020 07:26:57 +0000Gontis28029 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/bessel-birth-death-process#commentsLong-range memory test by the burst and inter-burst duration distribution
https://www3.unifr.ch/econophysics/?q=content/long-range-memory-test-burst-and-inter-burst-duration-distribution
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p> It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying values of the Hurst exponent. We propose the burst and inter-burst duration statistical analysis as one more test of long-range memory and implement it with the limit order book data comparing it with other widely used estimators. This method gives a more reliable evaluation of the Hurst exponent independent of the stock in consideration or time definition used. Results strengthen the expectation that burst and inter-burst duration analysis can serve as a better method to investigate the property of long-range memory.</p>
</div></div></div>Thu, 04 Jun 2020 07:19:05 +0000Gontis28028 at https://www3.unifr.ch/econophysicshttps://www3.unifr.ch/econophysics/?q=content/long-range-memory-test-burst-and-inter-burst-duration-distribution#comments