Varying-Coefficient Stochastic Differential Equations with Applications in Ecology

Théo Michelot (), Richard Glennie, Catriona Harris and Len Thomas
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Théo Michelot: University of St Andrews
Richard Glennie: University of St Andrews
Catriona Harris: University of St Andrews
Len Thomas: University of St Andrews

Journal of Agricultural, Biological and Environmental Statistics, 2021, vol. 26, issue 3, No 7, 446-463

Abstract: 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 phenomenon 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 nonparametric functions of covariates, similar to generalized additive models. Combining the SDE and nonparametric 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. Supplementary materials accompanying this paper appear online.

Keywords: Continuous time; Diffusion process; Nonparametric; Smoothing splines; Generalized additive models; Animal movement (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13253-021-00450-6

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