Abstract
Self-organization occurs when a system shows distinct shifts in dynamics due to variations in the parameters that govern the system. Relatedly, many human dynamic processes with self-organizing features comprise subprocesses that unfold across multiple time scales. Incorporating time-varying parameters (TVPs) into a dynamic model of choice provides one way of representing self-organization as well as multi-time scale processes. Extant applications involving models with TVPs have been restricted to formulation in discrete time. Related work for representing TVPs in continuous-time models remains scarce. We propose a stochastic differential equation (SDE) modeling framework with TVPs as a way to capture self-organization in continuous time. We present several examples of SDEs with TVPs, including a stochastic damped oscillator model with hypothesized functional shifts in both set points and damping. Furthermore, we discuss plausible models that may be used to approximate changes in the TVPs in the absence of further knowledge concerning their true change mechanisms.
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- 1.
The current version of dynr outputs Wald-type confidence intervals based on the standard errors of the (transformed) parameters. Wald-type confidence intervals are known to be inaccurate for variance parameters, particularly when the variance is near zero. The dynr team is working on options of other types of confidence interval estimates.
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Chen, M., Chow, SM., Hunter, M.D. (2018). Stochastic Differential Equation Models with Time-Varying Parameters. In: van Montfort, K., Oud, J.H.L., Voelkle, M.C. (eds) Continuous Time Modeling in the Behavioral and Related Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-77219-6_9
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