Abstract
A key feature of agent-based modeling is the understanding of the macroscopic behavior based on data at the microscopic level. In this respect, financial market models are requested to replicate, at the aggregate level, the stylized facts of empirical data. Among them, a remarkable role is played by the long term behavior. Indeed, the study of the long-term memory is relevant, in that it describes if and how past events continue to maintain their influence for the future evolution of a system. In economic applications, this is relevant for understanding the reaction of the system to micro- and macro-economic shocks. Moreover, further information on the long-term memory properties of a system can be obtained by analyzing agents heterogeneity and the outcome of their aggregation. The aim of this paper is to review a few techniques—though the most relevant in our opinion—for studying the long-term memory as emergent property of systems composed by heterogeneous agents. Theorems relevant to the present analysis are summarized and their applications in four structural models with long-term memory are shown. This property is assessed through the analysis of the functional relation between model parameters.
Highlights
The presence of long-term memory is a remarkable feature of time series, which are eventually generated by stochastic processes, when the autocorrelation function decays hyperbolically as the time lag increases
In [21], we provide a mathematically tractable financial market model that can give an insight on the market microstructure that captures some characteristics of financial time series
In [22], we focus on the long memory of prices and returns of an asset traded in a financial market
Summary
The presence of long-term memory is a remarkable feature of time series, which are eventually generated by stochastic processes, when the autocorrelation function decays hyperbolically as the time lag increases. In assessing the long-term memory property, a key role is played by the presence of heterogeneity in the agent-based model In this respect, for what concerns the specific contest of finance, the interaction among agents leads to an imitative behavior, that can affect the structure of the asset price dynamics. The keypoint of the quoted references is to assume distributional hypothesis on parameters of models in order to detect the presence of long-term memory in time series It is worth citing [29], from which the present report differs: [29] is targeting to provide a model while we propose here a review on some theoretical probabilistic methods.
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