Modeling the persistent volatility of asset returns

Empirical evidence suggests that the volatility of financial asset returns displays some type of persistence that cannot be appropriately modeled within the classical GARCH setting. Two alternative frameworks have been recently suggested to incorporate this type of persistence: fractionally integrated models, such as the Long Memory Stochastic Volatility (LMSV) model, and regime-switching schemes, such as the regime switching ARCH (SWARCH). A switching stochastic volatility model (SWSV) is a convenient and flexible alternative which can be directly compared with the LMSV model. Asymptotically, the autocorrelation functions of switching regime and long-memory models have quite distinct behavior. This fact can help the researcher to make the appropriate choices in face of empirical data.