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 behavioural 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 (Technical Report. CeNDEF working paper 03-05, University of Amsterdam. Tinbergen Institute Discussion Paper 2003-073/1). 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 coefficient. A-synchronous 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.