This paper considers a simple Continuous Beliefs System (CBS) toinvestigate the effects on price dynamics of several behavioralassumptions: (i) herd behaviour; (ii) a-synchronous updating ofbeliefs; and (iii) heterogeneity in time horizons (memory) amongagents. The recently introduced concept of a CBS allows one to model the co-evolution of prices and the beliefs distribution explicitly, while keeping track of the unpredictable nature of individual preferences (Diks and Van der Weide, 2003). As a benchmark model we take a simple CBS, which in a market withmany traders exhibits a random walk driven by news.Using the explicit nature of the dynamics of the CBS we show that the introduction of herding modifies the random walk to an ARIMA($0,1,1$) process, which is observationally equivalent to areduction of the number of market participants. In terms of returns the model predicts MA(1) structure with a negative coeffient. Asynchronous updating leads to an MA(1) model for returns with GARCH($1,1$) innovations, and predicts a relation between the ARCH and GARCH coefficients. Heterogeneity in memory leads to long-range dependence in returns. In the empirical section we perform a modest `reality check' concerning the predicted sign of the MA coefficient and the relation between the ARCH and GARCH coefficients for exchange rate data.
Continuous beliefs systems Random dynamical systems Heterogeneity Herding ARIMA GARCH Long-range dependence