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Extra info for Custom PC (September 2015)
We showed the scaled discrete time process converges to a superposition of a Brownian motion and countably infinite number of fractional Brownian motions with Hurst exponents greater than one-half. We note that the number of hidden orders randomly varies, that Hurst exponents are not bounded 4 Signs of Market Orders and Human Dynamics 41 above and that the maximum Hurst exponent of obtained process depends on hidden order of medium size. ˝n ; Pn /, where n is a natural number. In the next section, we will define a discrete time stochastic process in time interval n D f1; 2; : : : ; ng which describes cumulative order signs on the probability space.
The former is a consequence of the top plot of Fig. 3 (the plots showing the lack of change in correlations is not shown due to space limitations), the latter is a consequence of the lower plot Fig. 3 for the Asian crisis crash (the plots showing the lack of change in transfer entropy are not shown). However, in the case of the Asian crash, the transfer entropy significantly peaked several days after the crisis but the significance of this is not clear from the data. This result is not peculiar to trading days in which known ‘significant’ events have occurred.
Lizier JT (2014) JIDT: an information-theoretic toolkit for studying the dynamics of complex systems. Front Robot AI 1:11. 00011 12. Radelet S, Sachs J (1998) The onset of the east asian financial crisis. Tech. , National bureau of economic research 13. Li W, Packard NH, Langton CG (1990) Physica D: Nonlinear Phenom 45(1):77 14. Kwon O, Yang JS (2008) EPL (Europhys Lett) 82(6):68003 15. Matsuda H, Kudo K, Nakamura R, Yamakawa O, Murata T (1996) Int J Theor Phys 35(4):839 Chapter 3 Execution and Cancellation Lifetimes in Foreign Currency Market Jean-François Boilard, Hideki Takayasu, and Misako Takayasu Abstract We analyze mechanisms of foreign currency market order’s annihilation with a focus on the lifetime of these orders.