CGMM LASSO-type estimator for the process of Ornstein–Uhlenbeck type

In this paper, we study the LASSO-type penalized CGMM (GMM with continuum of moment method) estimator for the process of Ornstein–Uhlenbeck type. This LASSO-type estimator is obtained by minimizing the summation of the CGMM object function and a LASSO-type penalty, which is included for model selection. In the proposed method, model selection and estimation are done simultaneously. Under some regularity conditions, the proposed estimator asymptotically follows a non-standard normal distribution (Caner, 2009). Simulation study shows that the proposed estimator correctly selects the true model much more frequently than the commonly used Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC).