The Combined Estimating Function Approach And Its Application In ACD Models

Efficiency is one of the most important topic in parametric estimation.The combined estimating function approach based on maximization of the Fisher’s information is a novel method for parametric estimation.The Autoregressive Conditional Duration(ACD)model,as a non-linear time series model for studying high frequency data in financial markets,plays an important role in describing market microstructure.Parametric estimation for the ACD model and other variant models has attracted more and more attention recently.In this thesis,based on the optimal estimating function defined by Godambe’s theorem,a combined estimating function approach is considered by combining two orthogonal optimal estimating functions to estimate the parameters of ACD and other variant models.First,the probability structure of the ACD model is studied,where existence of a unique stationary solution and ergodicity of the ACD model are proven,and the conditional expectation can be written as an infinite linear sum of the previous observations uniquely.Then by constructing the infinite linear sum of the previous observations,combined estimating functions of the ACD model and its variant models are given.Finally,a simulation example is given to compare the performance between the finite linear form of the model and the original ACD model.