State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

Ourania Theodosiadou and George Tsaklidis
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Ourania Theodosiadou: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
George Tsaklidis: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Mathematics, 2021, vol. 9, issue 16, 1-13

Abstract: State space model representation is widely used for the estimation of nonobservable (hidden) random variables when noisy observations of the associated stochastic process are available. In case the state vector is subject to constraints, the standard Kalman filtering algorithm can no longer be used in the estimation procedure, since it assumes the linearity of the model. This kind of issue is considered in what follows for the case of hidden variables that have to be non-negative. This restriction, which is common in many real applications, can be faced by describing the dynamic system of the hidden variables through non-negative definite quadratic forms. Such a model could describe any process where a positive component represents “gain”, while the negative one represents “loss”; the observation is derived from the difference between the two components, which stands for the “surplus”. Here, a thorough analysis of the conditions that have to be satisfied regarding the existence of non-negative estimations of the hidden variables is presented via the use of the Karush–Kuhn–Tucker conditions.

Keywords: state space model; Kalman filter; constrained optimization; two-sided components (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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