Nonlinear Parameter Estimation for State-Space ARCH Models with Missing Observations

摘要

A new mathematical representation, based on a discrete time nonlinear state space formulation, is presented to characterize AutoRegresive Conditional Heteroskedasticity (ARCH) models. A novel parameter estimation procedure for state-space ARCH models with missing observations, based on an Extended Kalman Filter (EKF) approach, is described and successfully evaluated herein. Finally, through a comparison analysis between our proposed estimation method and a Quasi Maximum Likelihood Estimation (QMLE) technique based on different methods of imputation, some numerical results with simulated data, which make evident the effectiveness and relevance of the proposed nonlinear estimation technique are given.