Volume 118, Number 3, May 2017
|Number of page(s)||7|
|Published online||07 July 2017|
Symbolic dynamics techniques for complex systems: Application to share price dynamics
Queen Mary University of London, School of Mathematical Sciences - Mile End Road, London E1 4NS, UK
Received: 15 June 2017
Accepted: 20 June 2017
The symbolic dynamics technique is well known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Our main example is the investigation of share price returns in a coarse-grained way. A nontrivial spectrum of Rényi 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 modelling based on non-Markovian stochastic processes. Our method allows for quantitative comparisons of entirely different complex systems, for example the statistics of symbol sequences generated by share price returns using 4 symbols can be compared with that of genomic sequences.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Tp – Time series analysis / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2017
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