Joint Estimation Using Quadratic Estimating Function

A class of martingale estimating functions is convenient and plays an important role for inference for nonlinear time series models. However, when the information about the first four conditional moments of the observed process becomes available, the quadratic estimating functions are more informative. In this paper, a general framework for joint estimation of conditional mean and variance parameters in time series models using quadratic estimating functions is developed. Superiority of the approach is demonstrated by comparing the information associated with the optimal quadratic estimating function with the information associated with other estimating functions. Themethod is used to study the optimal quadratic estimating functions of the parameters of autoregressive conditional duration ACD models, random coefficient autoregressive RCA models, doubly stochastic models and regressionmodels with ARCH errors. Closed-form expressions for the information gain are also discussed in some detail.