Modeling of the parties' vote share distributions

Competition between varying ideas, people and institutions fuels the dynamics of socio-economic systems. Numerous analyses of the empirical data extracted from different financial markets have established a consistent set of stylized facts describing statistical signatures of the competition in the financial markets. Having an established and consistent set of stylized facts helps to set clear goals for theoretical models to achieve. Despite similar abundance of empirical analyses in sociophysics, there is no consistent set of stylized facts describing the opinion dynamics. In this contribution we consider the parties' vote share distributions observed during the Lithuanian parliamentary elections. We show that most of the time empirical vote share distributions could be well fitted by numerous different distributions. While discussing this peculiarity we provide arguments, including a simple agent-based model, on why the beta distribution could be the best choice to fit the parties' vote share distributions.Comment: 12 pages, 7 figure

Empirical analysis and agent-based modeling of Lithuanian parliamentary elections

In this contribution we analyze a parties' vote share distribution across the polling stations during the Lithuanian parliamentary elections of 1992, 2008 and 2012. We find that the distribution is rather well fitted by the Beta distribution. To reproduce this empirical observation we propose a simple multi-state agent-based model of the voting behavior. In the proposed model agents change the party they vote for either idiosyncratically or due to a linear recruitment mechanism. We use the model to reproduce the vote share distribution observed during the election of 1992. We discuss model extensions needed to reproduce the vote share distribution observed during the other elections.Comment: 19 pages, 11 figure

Consentaneous agent-based and stochastic model of the financial markets

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.Comment: 17 pages, 6 figures, Gontis V, Kononovicius A (2014) Consentaneous Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7): e102201. doi: 10.1371/journal.pone.010220

Three-state herding model of the financial markets

We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability density function of the absolute returns we are able to reproduce the fractured power spectral density, which is observed in the high-frequency financial market data. Given example of consistent agent-based and stochastic modeling will provide background for the further developments in the research of complex social systems.Comment: 11 pages, 3 figure

Agent based reasoning for the non-linear stochastic models of long-range memory

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. Agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.Comment: 10 pages, 3 figure

Empirical Survival Jensen-Shannon Divergence as a Goodness-of-Fit Measure for Maximum Likelihood Estimation and Curve Fitting

The coefficient of determination, known as R2, is commonly used as a goodness-of-fit criterion for fitting linear models. R2 is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fitting a parametric distribution to a data set using, say, the maximum likelihood estimation method. A general approach to measure the goodness-of-fit of the fitted parameters, which is advocated herein, is to use a non- parametric measure for comparison between the empirical distribution, comprising the raw data, and the fitted model. In particular, for this purpose we put forward the Survi- val Jensen-Shannon divergence (SJS) and its empirical counterpart (ESJS) as a metric which is bounded, and is a natural generalisation of the Jensen-Shannon divergence. We demonstrate, via a straightforward procedure making use of the ESJS, that it can be used as part of maximum likelihood estimation or curve fitting as a measure of goodness-of-fit, including the construction of a confidence interval for the fitted parametric distribution. Furthermore, we show the validity of the proposed method with simulated data, and three empirical data sets