GARCH Models Estimation with Missing Observations Using State Space Representation

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Natalia Bahamonde*+ and Sebastián Ossandón
• Companies: Pontificia Universidad Católica de Valparaiso and Pontificia Universidad Católica de Valparaíso
• Keywords: GARCH models ; missing observations ; Extender Kalman Filter ; Nonlinear state space model

Abstract

A new mathematical representation, based on a discrete time nonlinear state space formulation, is presented to characterize Generalized AutoRegresive Conditional Heteroskedasticity (GARCH) models. In order to improve the parameter and state estimation techniques in GARCH models, a novel estimation procedure for nonlinear time series model 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 nonlinear estimation method and a Quasi Maximum Likelihood Estimation (QMLE) technique based on different methods of imputation, some numerical results with real data, which make evident the effectiveness and relevance of the proposed nonlinear estimation technique are given.