Estimation of time-varying parameters in deterministic dynamic models

In this paper, we develop local polynomial estimation procedures to fit deterministic dynamic models with a focus on the estimation of time-varying parameters. Three local estimation methods for estimating time-varying parameters are proposed: two-step local linear estimation, two-step local quadratic estimation, and a two-step local hybrid method. Although the proposed estimation methods are applicable for general dynamic models, we establish the asymptotic properties of the proposed estimators for a linear deterministic dynamic model and show that the proposed estimators for linear dynamic models achieve the optimal convergence rate. Simulation studies reveal that the proposed two-step estimation met hods perform better than the naive one-step local estimator. An application from all AIDS clinical trial is presented to illustrate the methodologies.