Abstract
GMM inference procedures based on the square of the modulus of the model characteristic function are developed using sample moments selected using estimating function theory and bypassing the use of empirical characteristic function of other GMM procedures in the literature. The procedures are relatively simple to implement and are less simulation-oriented than simulated methods of inferences yet have the potential of good efficiencies for models with densities without closed form. The procedures also yield better estimators than method of moment estimators for models with more than three parameters as higher order sample moments tend to be unstable.
Highlights
IntroductionData analysts often have to use distributions with density functions having complicated forms
Introduction and an Overview of GMMProcedures Based on Empirical Characteristic Function
GMM inference procedures based on the square of the modulus of the model characteristic function are developed using sample moments selected using estimating function theory and bypassing the use of empirical characteristic function of other GMM procedures in the literature
Summary
Data analysts often have to use distributions with density functions having complicated forms. They are often expressed using mean of series representations but model characteristic functions are simpler and have closed form expressions. The compound Poisson distributions are classical examples and for finance, the stable distributions fall into the same category. These are infinitely divisible and many infinitely divisible distributions share the same property of having much simpler characteristic functions
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