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State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

Author

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  • Ourania Theodosiadou

    (Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
    These authors contributed equally to this work.)

  • George Tsaklidis

    (Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Ourania Theodosiadou & George Tsaklidis, 2021. "State Space Modeling with Non-Negativity Constraints Using Quadratic Forms," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1908-:d:612018
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    References listed on IDEAS

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    1. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    2. Timothy Cogley & Thomas J. Sargent, 2002. "Evolving Post-World War II US Inflation Dynamics," NBER Chapters, in: NBER Macroeconomics Annual 2001, Volume 16, pages 331-388, National Bureau of Economic Research, Inc.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. Ourania Theodosiadou & Sotiris Skaperas & George Tsaklidis, 2017. "Change Point Detection and Estimation of the Two-Sided Jumps of Asset Returns Using a Modified Kalman Filter," Risks, MDPI, vol. 5(1), pages 1-14, March.
    5. Ourania Theodosiadou & George Tsaklidis, 2017. "Estimating the Positive and Negative Jumps of Asset Returns Via Kalman Filtering. The Case of Nasdaq Index," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1123-1134, December.
    6. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
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    Cited by:

    1. Papageorgiou, Vasileios E. & Tsaklidis, George, 2023. "An improved epidemiological-unscented Kalman filter (hybrid SEIHCRDV-UKF) model for the prediction of COVID-19. Application on real-time data," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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