CMARS GMM estimation for semi-parametric models by conic optimization

Abstract

The well-known Generalized Method of Moments (GMM) estimation methodology has been evaluated in various specifications. We propose a novelity in GMM estimation by introducing Conic Quadratic Programming (CQP). The proposed model builds up a flexible tool to model financial data. In our study, we first derive and explain our model specifications (semi parametric model). We identify the moment conditions, that are satisfied by the unknown parameters of the model. These moment conditions are determined by the implementation of Conic Quadratic Optimization. In order to generalize our model for the process, which has infinite number of observations, we proof that our model conditions are efficient and consistent. It is shown that consistency can be achieved through convergence of the model parameters towards the true parameters. By the help of Tikhonov regularization, we construct a minimum distance measure and identify the conditions under which convergence is achieved. Asymptotic distribution of the CQP-estimated GMM estimator is evaluated based on the variance-covariance matrix.