STAGE Spatio-temporal classification of China’s stocks based on Rényi difference matrix

Subject Proposal
We propose to develop a method to perform quantitative comparisons of different complex subsystems 1 from China’s
stock index for different given spatio-temporal scales by encoding the subsystems'observed data in their respective
symbolic dynamic space.
This method must enable to define a classification matrix of the studied subsystems'behaviors dynamics and arise
cluster of subsystems that share common similarities regarding their complex behaviors, and thus, according to given
spatio-temporal scales.
In particular, this research will rely on previous researches made by:
- Dan Xu and Professor Christian Beck regarding their work on their application of symbolic dynamics
techniques to share price dynamics [1].
- Professor Christian Beck and Professor F. Schögl regarding their study of Thermodynamics'behaviors of
Chaotic System [2].
- C.E. Shannon regarding his work on the Theory of Communication and Information, especially its
relationship with the Symbolic Dynamic Theory [3].
- Professor Hao Bai-Lin regarding his work on Symbolic Dynamic and Chaos in Dissipative Systems [4].
- Professors Hadrien Salat, Roberto Murcio, and Elsa Arcaute regarding their work on Multifractal
methodology [5].
- Professors Yihong Wu, Sergio Vurdu regarding their work on the Rényi Information Dimension [6].
- We can also use my recent work regarding the application of Symbolic Dynamic and Information Theory to
measure the degree of complexity arising from economic time series [7].
Problematic
At the end of this research, we must be able to know what China’s stocks might be governed by similar dynamics and
on which time scales. By dynamics we mean:
- What is the degree of non-Markovian process for each stock and for given timescales?
- What is the degree of predictability of each stock on given timescales?
- What is the difference of dynamics'behaviors (i.e. complexity measures by the Rényi entropy) between each
stock and for given timescales?
- What type and group of stock provide the less information (in the sense of Shannon) on its future behaviors
and for given timescales?
Answer, Solution
By being able to answer these previous questions, we should be able to provide strong quantitative answers regarding
fundamentals topics in quantitative research namely:
- On what individual or group of stocks from China’s Index, “volatility models”, “noise models or “flow
trading strategies might be suitable to apply, and regarding which timescales?