Abstract:
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Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. Most widely-used SDEs are specified in terms of just a few parameters to allow for tractability, which can be limiting to capture detailed features of the data-generating process. We propose modelling the parameters as nonparametric functions of covariates, similar to generalized additive models, to allow for time-varying dynamics while retaining the simple interpretation of parametric models. We describe a computationally-efficient implementation based on the R packages mgcv and TMB, and we demonstrate the utility of the approach with applications in ecology, where there is often a trade-off between interpretability and flexibility.
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