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In ecology it is common for processes to be bounded based on physicalconstraints of the system. One common example is the positivity constraint,which applies to phenomena such as duration times, population sizes, and totalstock of a system's commodity. In this paper, we propose a novel method forembedding these dynamical systems into a lognormal state space model using anapproach based on moment matching. Our method enforces the positivityconstraint, allows for embedding of arbitrary mean evolution and variancestructure, and has a closed-form Markov transition density which allows formore flexibility in fitting techniques. We discuss two existing lognormal statespace models, and examine how they differ from the method presented here. Weuse 180 synthetic datasets to compare the forecasting performance under modelmisspecification and assess estimability of precision parameters between ourmethod and existing methods. We find that our models well undermisspecification, and that fixing the observation variance both helps toimprove estimation of the process variance and improves forecast performance.To test our method on a difficult problem, we compare the predictiveperformance of two lognormal state space models in predicting Leaf Area Indexover a 151 day horizon by embedding a process-based ecosystem model. We findthat our moment matching model performs better than its competitor, and isbetter suited for long predictive horizons. Overall, our study helps to informpractitioners about the importance of embedding sensible dynamics when usingmodels complex systems to predict out of sample.

Embedding Positive Process Models into Lognormal Bayesian State Space Frameworks using Moment Matching