On the specification of noise in two agent-based asset pricing models

The paper is concerned with two recent agent-based models of speculative dynamics from the literature, one by Gaunersdorfer and Hommes (2007) and the other by He and Li (2007). At short as well as long lags, both of them display an autocorrelation structure in absolute and squared returns that comes fairly close to that of real data at a daily frequency. The note argues that these long memory effects are to be ascribed to the stochastic specification of the price equation, which despite the wide fluctuations in these models fails to normalize the price shocks. Under an appropriate respecification, the long memory completely disappears. It is subsequently shown that an alternative introduction of randomness, which may be called structural stochastic volatility, can restore the original properties and even improves upon them.