Title: Multi-scale modelling of time series data using state-switching varying-coefficient stochastic differential equations
Authors: Timo Adam - University of Copenhagen (Denmark) [presenting]
Abstract: Varying-coefficient stochastic differential equations (SDEs) are popular tools for uncovering mechanistic relationships underlying time series data. By modelling the parameters of the process of interest as smooth functions of covariates, they provide an extension of basic SDEs that allows us to capture more detailed, non-stationary features of the data-generating process. However, in practice, these parameters often vary at multiple time scales, which is illustrated using dive data of beaked whales: while changes in pitch and roll exhibited within some dives can be described by some varying-coefficient SDE, other dives can be better characterised by other varying-coefficient SDEs; a pattern that is not readily accommodated for by the existing approach. We propose state-switching varying-coefficient SDEs as a novel class of statistical models for time series that accounts for such state-switching patterns between dives while simultaneously allowing us to make inferences on the underlying behavioural processes that occur within dives.