Nonlinear models for autoregressive conditional heteroskedasticity

This paper contains a brief survey of nonlinear models of autoregressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation are discussed. Forecasting volatility with nonlinear models is considered. Finally, parametric nonlinear models based on multiplicative decomposition of the variance receive attention.