Constrained Kalman Filtering: Additional Results

Adrian Pizzinga

International Statistical Review, 2010, vol. 78, issue 2, 189-208

Abstract: This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation. Cet article traite des modèles espace‐état sujets aux restrictions linéaires générales sur le vecteur d'état. La discussion se concentre autour de quatre aspects: le filtrage de Kalman restreint versus l'estimateur de moindres carrés restreint recursive; une nouvelle preuve du filtrage de Kalman restreint sous le cadre de l'espérance conditionelle; restrictions linéaires aux modèles espace‐état réduits; et la prédiction d'état sous restrictions linéaires. Les techniques proposées sont illustrées par deux problèmes réels. Le premier problème est concerné par l'analyse d'investissement sous un modèle à facteur dynamique, tandis que le second concerne les prédictions restreintes dans l'estimation de benchmarking.

Date: 2010
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