Bubbles and long-range dependence in asset prices volatilities

A model for a financial asset is constructed with two types of agents. The agents differ in terms of their beliefs. The proportions of the two types change over time according to a stochastic process which models the interaction between the agents. Thus, unlike other models, agents do not persist in holding "wrong" beliefs. Bubble-like phenomena in the assetprice occur. We consider several tests for detecting long range dependence and change-points in the conditional variance process. Although the model seems to generate long-memory properties of the volatility series, we show that this is due to the switching of regimes which are detected by the tests we propose.