Asymmetric Tsallis distributions for modelling financial market dynamics
arXiv:2102.04532 · doi:10.1016/j.physa.2021.126109
Abstract
Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For small time scales (delays), a good fit to the distributions of stock returns is obtained with q-Gaussian distributions, which can be derived either from Tsallis statistics or superstatistics. These distributions are symmetric. However, as the time lag increases, the distributions become increasingly non-symmetric. In this work, we address this problem by considering the data distribution as a linear combination of two independent normalized distributions - one for negative returns and one for positive returns. Each of these two independent distributions are half q-Gaussians with different non-extensivity parameter q and temperature parameter beta. Using this model, we investigate the behavior of stock market returns over time scales from 1 to 80 days. The data covers both the .com bubble and the 2008 crash periods. These investigations show that for all the time lags, the fits to the data distributions are better using asymmetric distributions than symmetric q-Gaussian distributions. The behaviors of the q parameter are quite different for positive and negative returns. For positive returns, q approaches a constant value of 1 after a certain lag, indicating the distributions have reached equilibrium. On the other hand, for negative returns, the q values do not reach a stationary value over the time scales studied. In the present model, the markets show a transition from normal to superdiffusive behavior (a possible phase transition) during the 2008 crash period. Such behavior is not observed with a symmetric q-Gaussian distribution model with q independent of time lag.
arXiv comment13 figures, 28 pages
References in corpus (18)
- Superstatistics
- Interpretation of the nonextensitivity parameter in some applications of Tsallis statistics and Lévy distributions
- Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
- Critical Market Crashes
- Nonextensive statistical mechanics and economics
- Measuring non-extensitivity parameters in a turbulent Couette-Taylor flow
- Dynamical model and nonextensive statistical mechanics of a market index on large time windows
- Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence
- On the small-scale statistics of Lagrangian turbulence
- Non-additivity of Tsallis entropies and fluctuations of temperature
- Statistical-thermodynamical foundations of anomalous diffusion
- Maximum Likelihood Estimation for q-Exponential (Tsallis) Distributions
- Fractal structure and non extensive statistics
- Transition from lognormal to chi-square superstatistics for financial time series
- Extended q-Gaussian and q-exponential distributions from Gamma random variables
- Non-extensive Behavior of a Stock Market Index at Microscopic Time Scales
- Financial Market Dynamics: Superdiffusive or not?
- Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure