Journal on Policy and Complex Systems
Given that , most of the papers published since then focused on : empirical evidences of long-range dependency in a wide set of different fields , from physics to finance ; on propositions that enhance the computational calculations of models which exhibit these stochastic properties and on the development of the theoretical mathematical toolset used to build and analyze such models .
Along the 1980s and 1990s , a set of econometric works was developed focusing basically on the origins of long memory processes as a result of the sum of cross-sectional short-memory processes , as can be seen in Granger ( 1980 ) and Lippi and Zaffaroni ( 1999 ); as result of the sum of continuous binary series as in Taqqu , Willinger , and Sherman ( 1997 ), where the governing cumulative distribution function of the binary states are governed by power laws ; structural changes / regime switching processes , as discussed in Stock and Watson ( 1996 ); and spatial Markov systems , as described in Beran ( 1994 ).
In addition to these theoretical studies , there exists a literature that use simulation approaches to study financial stylized facts and statistical properties , such as Brock and LeBaron ( 1996 ) and Farmer , Patelli , and Zovko ( 2005 )— which studied zero intelligence agents , resembling some of the primary objectives of this present study ; and Liu , Gregor , and Yang ( 2008 )— these authors studied effects of behavioral and structural assumptions in artificial stock markets . In line with them , this present study aims to complement this discussion .
Therefore , to achieve such goal , the authors aim to analyze processes from other viewpoints than those discussed above , with a special focus on the complex systems characteristics such as the agents ’ behavior , competition rules , and laws of motion , but still , discussing the Markovian properties of the models , whenever necessary to explain eventual asymptotic behaviors .
That said , the main idea of this paper is to discuss possible origins of such phenomena by running computational simulations of the interactions between single individuals ( called agents ), which produce local and global interactions that are studied in terms of its complexity features , instead of focusing on eventual generalization of convergence properties of its stochastic properties . Moreover , this paper aims to show and discuss that long memory properties are not necessarily resultant from long memory behavior of individual agents nor from social / economic frictions — in line with previous findings . Furthermore , it aims to extend the knowledge about complex systems and long memory processes ( initially restricted to heterogeneity ), by adding two other important factors : spatial complexity and large deviations from stationary states implied in the motion laws .
Spatial complexity , here , is directly linked to the spatial dispersion of resources and their respective availability , which of course will affect the state transition probabilities that the authors analyze , such as wealth inequality ( discussed in the third example ), in terms
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