Nonlinear recursive estimation of volatility via estimating functions

For certain volatility models, the conditional moments that depend on the parameter are of interest. Following Godambe and Heyde (1987), the combined estimating function method has been used to study inference when the conditional mean and conditional variance are functions of the parameter of interest (See Ghahramani and Thavaneswaran [Combining Estimating Functions for Volatility. Journal of Statistical Planning and Inference, 2009, 139, 1449–1461] for details). However, for application purposes, the resulting estimates are nonlinear functions of the observations and no closed form expressions of the estimates are available. As an alternative, in this paper, a recursive estimation approach based on the combined estimating function is proposed and applied to various classes of time series models, including certain volatility models.