Superstatistics and symbolic dynamics of share price returns on different time scales
Abstract
Share price returns on different time scales can be well modeled by a superstatistical
dynamics. We provide an investigation which type of superstatistics is most suitable
to properly describe share price dynamics on various time scales. It is shown
that while chi-square-superstatistics works well on a time scale of days, on a much
smaller time scale of minutes the price changes are better described by lognormal
superstatistics. The system dynamics thus exhibits a transition from lognormal
to chi-square-superstatistics as a function of time scale. We discuss a more general
model interpolating between both statistics which fits the observed data very
well. We also present results on correlation functions of the extracted superstatistical
volatility parameter, which exhibits exponential decay for returns on large time
scales, whereas for returns on small time scales there are long-range correlations
and power-law decays.
We also apply the symbolic dynamics technique from dynamical system theory
to analyse the coarse-grained evolution of share price returns. A nontrivial spectrum
of Renyi entropies is found. We study how the spectrum depends on the time scale
of returns, the sector of stocks considered, as well as the number of symbols used
for the symbolic description. Overall our analysis confirms that in the symbol space
transition probabilities of observed share price returns depend on the entire history
of previous symbols, thus emphasizing the need for a model of share price evolution
based on non-Markovian stochastic processes. Our method allows for quantitative
comparisons of entirely different complex systems, for example the statistics of
coarse-grained share price returns using 4 symbols can be compared with that of
other complex systems.
Authors
Xu, DanCollections
- Theses [4122]