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The estimation of a state space model by estimating functions with an application
Author(s) -
Papanastassiou Demetrios,
Ioannides Demetrios
Publication year - 2004
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2004.00268.x
Subject(s) - estimator , gaussian , mathematics , stochastic volatility , state space , state space representation , estimation , state (computer science) , state vector , likelihood function , maximum likelihood , mathematical optimization , volatility (finance) , estimation theory , computer science , algorithm , econometrics , statistics , physics , management , quantum mechanics , classical mechanics , economics
Conventionally the parameters of a linear state space model are estimated by maximizing a Gaussian likelihood function, even when the input errors are not Gaussian. In this paper we propose estimation by estimating functions fulfilling Godambe's optimality criterion. We discuss the issue of an unknown starting state vector, and we also develop recursive relations for the third‐ and fourth‐order moments of the state predictors required for the calculations. We conclude with a simulation study demonstrating the proposed procedure on the estimation of the stochastic volatility model. The results suggest that the new estimators outperform the Gaussian likelihood.