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arXiv · 2008.09111

Varying-coefficient stochastic differential equations with applications in ecology

Théo Michelot·Richard Glennie·Catriona Harris·Len Thomas
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Abstract

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their parameters often have a clear interpretation. These advantages come at the cost of requiring a relatively simple model specification. We propose a flexible model for SDEs with time-varying dynamics where the parameters of the process are non-parametric functions of covariates, similar to generalized additive models. Combining the SDEs and non-parametric approaches allows for the SDE to capture more detailed, non-stationary, features of the data-generating process. We present a computationally efficient method of approximate inference, where the SDE parameters can vary according to fixed covariate effects, random effects, or basis-penalty smoothing splines. We demonstrate the versatility and utility of this approach with three applications in ecology, where there is often a modelling trade-off between interpretability and flexibility.

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Théo Michelot, Richard Glennie, Catriona Harris, Len Thomas. 2020-08-20. Varying-coefficient stochastic differential equations with applications in ecology. https://arxiv.org/abs/2008.09111

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