Stylized Facts of Financial Time Series and Three Popular Models of Volatility

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MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL (2009, methodology): “Other models such as the GARCH and the EGARCH models are not able to reproduce adequately the previously mentioned stylized facts of financial time series; see Malmsten and Teräsvirta (2004) and Carnero, Peña, and Ruiz (2004) for comprehensive discussions.”
Realized Volatility: A Review (2008, background): “However, as observed by Bollerslev (1987), Malmsten and Teräsvirta (2004), and Carnero et al. (2004), among others, most of the latent volatility models fail to describe satisfactorily several stylized facts that are observed in financial time series.”