Econophysics Forum
http://www3.unifr.ch/econophysics
enOn Forecasts of the COVID-19 Pandemic
http://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 maximum likelihood 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 1.36. 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 http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/forecasts-covid-19-pandemic#commentsModel of continuous random cascade processes in financial markets
http://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 http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/model-continuous-random-cascade-processes-financial-markets#commentsAn Elementary Humanomics Approach to Boundedly Rational Quadratic Models
http://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 http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/elementary-humanomics-approach-boundedly-rational-quadratic-models#commentsBoundedly-Rational Fast-Tuning Control Theory and Statistical Mechanics
http://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 http://www3.unifr.ch/econophysicshttp://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
http://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 http://www3.unifr.ch/econophysicshttp://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
http://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 http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/consentaneous-model-financial-markets-exhibiting-spurious-nature-long-range-memory#commentsBessel-like birth-death process
http://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 http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/bessel-birth-death-process#commentsLong-range memory test by the burst and inter-burst duration distribution
http://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 http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/long-range-memory-test-burst-and-inter-burst-duration-distribution#commentsInformation Cascades and the Collapse of Cooperation
http://www3.unifr.ch/econophysics/?q=content/information-cascades-and-collapse-cooperation
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div>
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<p>In various types of structured communities newcomers choose their interaction partners by selecting a role-model and copying their social networks. Participants in these networks may be cooperators who contribute to the prosperity of the community, or cheaters who do not and simply exploit the cooperators. For newcomers it is beneficial to interact with cooperators but detrimental to interact with cheaters. However, cheaters and cooperators usually cannot be identified unambiguously and newcomers’ decisions are often based on a combination of private and public information. We use evolutionary game theory and dynamical networks to demonstrate how the specificity and sensitivity of those decisions can dramatically affect the resilience of cooperation in the community. We show that promiscuous decisions (high sensitivity, low specificity) are advantageous for cooperation when the strength of competition is weak; however, if competition is strong then the best decisions for cooperation are risk-adverse (low sensitivity, high specificity). Opportune decisions based on private and public information can still support cooperation but suffer of the presence of information cascades that damage cooperation, especially in the case of strong competition. Our research sheds light on the way the interplay of specificity and sensitivity in individual decision-making affects the resilience of cooperation in dynamical structured communities.</p>
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</div></div></div>Fri, 22 May 2020 08:40:01 +0000mcavaliere28027 at http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/information-cascades-and-collapse-cooperation#commentsPotential in the Schrodinger equation: estimation from empirical data
http://www3.unifr.ch/econophysics/?q=content/potential-schrodinger-equation-estimation-empirical-data
<div class="field field-name-abstract field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>A recent model for the stock market calculates future price distributions of a stock as a wave function of a quantum particle conﬁned in an inﬁnite potential well. In such a model the question arose as to how to estimate the classical potential needed for solving the Schrodinger equation. In the present article the method used in that work for evaluating the potential is described, in the simplest version to implement, and more sophisticated implementations are suggested later.</p>
</div></div></div>Mon, 23 Mar 2020 09:34:48 +0000jlsubias28026 at http://www3.unifr.ch/econophysicshttp://www3.unifr.ch/econophysics/?q=content/potential-schrodinger-equation-estimation-empirical-data#comments