Herding, A-synchronous Updating and Heterogeneity in Memory in a CBS

This paper considers a simple Continuous Beliefs System (CBS) to investigate the effects on price dynamics of several behavioral assumptions: (i) herd behaviour; (ii) a-synchronous updating of beliefs; and (iii) heterogeneity in time horizons (memory) among agents. 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 with many 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 a reduction 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.