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Parameter estimation in a simple stochastic differential equation for phytoplankton modelling

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  • Møller, Jan Kloppenborg
  • Madsen, Henrik
  • Carstensen, Jacob

Abstract

The use of stochastic differential equations (SDEs) for the simulation of aquatic ecosystems has attracted increasing attention in recent years. The SDE setting also provides the opportunity for statistical estimation of ecosystem parameters. We present an estimation procedure, based on Kalman filtering and likelihood estimation, which has proven useful in other fields of application. The estimation procedure is presented and the development from ordinary differential equations (ODEs) to SDEs is discussed with emphasis on autocorrelated residuals, commonly encountered with ODEs. The estimation procedure is applied to a simple nitrogen-phytoplankton model, with data from a Danish estuary (1988–2006). The resulting SDE is simple enough to have a well-known stationary distribution and this distribution is presented and compared with observed phytoplankton data.

Suggested Citation

  • Møller, Jan Kloppenborg & Madsen, Henrik & Carstensen, Jacob, 2011. "Parameter estimation in a simple stochastic differential equation for phytoplankton modelling," Ecological Modelling, Elsevier, vol. 222(11), pages 1793-1799.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:11:p:1793-1799
    DOI: 10.1016/j.ecolmodel.2011.03.025
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    References listed on IDEAS

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    1. Luschgy, Harald & Pagès, Gilles, 2006. "Functional quantization of a class of Brownian diffusions: A constructive approach," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 310-336, February.
    2. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.
    3. João Nicolau, 2002. "A new technique for simulating the likelihood of stochastic differential equations," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 91-103, June.
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