Price fluctuations in speculative market dynamics have interesting statistical properties. As temporal ones, (I) vanishing autocorrelation of return, (ii) intermittency and long-memory in the magnitude of return, called volatility,(iii) self-similarity of volatilities for different time-scales ("volatility cascade "). These properties in strongly correlated regime from minutes to months are crucial for understanding market and to control risk. First, it is briefly reviewed how one can characterize the statistical properties of such non-equilibrium nature. Second, adaptive agent models with opinion-epidemics and speculative bubbles are considered including Lux's stochastic model. The origin of volatility clustering and cascade might be understood as aggregate behavior of human speculations, and the dynamics might be regareded as a kind of on-off intermittency.