Financial time series obtained by agent-based simulation

Abstract

Economic news often talks about growths and drops of indexes and individual stocks, but many people (including me before I did this work) do not understand neither how the stock market works nor what causes its price fluctuations. Stock markets are complex systems. In empirical sciences, a common strategy used to study a real system consists in making simplified models that keep their main features, and analyze them in order to understand further the system dynamics. There is a type of models known as agent-based models that are used to simulate complex systems by creating software objects (called agents) whose behavior have global consequences for the system. This concept allows modelers to connect the micro-level of individuals with the macroscopic patterns, what is essential to understand systems interactions. One example of agent-based environment and programming language is NetLogo, created by Uri Wilensky in 1999. Since individual investors’ decisions control the dynamics of stock markets, it seems reasonable to treat the stock market as if it is a dynamic system of interacting agents, that will represent investors. The collective behavior of these investors, each of which acts independently, produces prive movements. Based on Silva’s (2014) Collective behavior in the Stock Market model, we have designed and implemented a model for the evolution of a very simple market, with a single asset price, using the NetLogo environment. On the other hand, companies’ share prices form time series. Statistics supplies powerful tools and methods to understand the processes behind time series, make a model of them and, furthermore, forecast future values based on the current data. Hence, financial time series analysis plays an important role in investments strategies and other economical applications. We are going to describe the main methods and models used for this kind of series, but there is so much bibliography on the statistical treatment of financial series; see, for example, Tsay (2005).