Long Memory Properties and Complex Systems
of a spatial Markov system , within a competition framework .
Large deviations from equilibria , here , refer to how they interact with the system ’ s laws of motion — these are derived from Markov properties , which , in turn , are derived from transition rules .
Consequently , the authors intend on bringing such discussion in order to establish and important connection between the classical results obtained by analyzing Markov processes and complex systems .
The importance of the present work is because the correct specification and understanding of stochastic processes are very important . Its specification affects the description of the autocorrelation structure , which is very relevant to a wide range of problems , such as asset pricing , macroeconomic modeling , social policy conduction — discussion about poverty and inequality and how they evolve in terms of the system ’ s properties — and other time series phenomena .
It is worth noticing that the misspecification of such features may induce very different results in long term , affecting the way that optimal policymaking may be conducted , since these effects last longer than short memory . In addition , it delivers useful insights while discussing different approaches on the concept of path-dependent phenomena and what should be expected if nothing is done if the competition itself does not solve the inequality problem .
To accomplish the goal of focusing in the agent ’ s environment , aiming to put this work into an interesting perspective for the discussion of policymaking , in all computational models here described , the agents must only explicitly have short-memory relationships with their respective past states — as in Farmer et al . ( 2005 ). Thus , it should be possible to show that long memory properties arise not because the agents may have a memory unit which guides them in their respective actions ( behavior ), as one may think in terms of traders pricing an asset according to the present and their perception of a fair price based on their long experience ; but as a result of the aggregate behavior of them , as a consequence of the complexity emergence , pointing back to the seminal works of Mandelbrot and Wallis ( 1969 ) and establishing an interesting link with the growing field of complexity , as in Wolfram ( 2002 ), Monteiro ( 2011 , 2014 ), among others .
Consequently , the state of agents in such systems would be somewhat affected by disturbances occurred in a far past , but not explicitly derived of individual long memory behavior , which affects directly the development of optimal control policies for such kind of systems .
Keeping that in mind , three different computational models are presented and simulated in this work , showing that long-range dependency may simply arise from the interactions between the agents , establishing what can be called “ long memory emergence .”
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