Capitulo de libro

### ON THE NONLINEAR ESTIMATION OF GARCH MODELS. USING AN EXTENDED KALMAN FILTER

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##### Author

Bahamonde Rozas, Natalia Carolina

Ossandon Veliz, Sebastian Eduardo

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##### Abstract

A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given.A new mathematical representation, based on a
discrete-time nonlinear state space formulation, is presented
to characterize a Generalized Auto Regresive Conditional Heteroskedasticity
(GARCH) model. Nonlinear parameter estimation
and nonlinear state estimation, for this state space model,
using an Extended Kalman Filter (EKF) are described. Finally
some numerical results, which make evident the effectiveness
and relevance of the proposed nonlinear estimation are given. FONDECYT FONDECYT