Journal of Probability and Statistics
Volume 2011 (2011), Article ID 372512, 14 pages
Research Article

Joint Estimation Using Quadratic Estimating Function

1Department of Statistics, University of Manitoba, 338 Machray Hall, Winnipeg, MB, Canada R3T 2N2
2University of Waterloo, Waterloo, ON, Canada N2L 2G1

Received 12 January 2011; Revised 10 March 2011; Accepted 11 April 2011

Academic Editor: Ricardas Zitikis

Copyright © 2011 Y. Liang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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. The method 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 regression models with ARCH errors. Closed-form expressions for the information gain are also discussed in some detail.