  Measurements of many biological processes are characterized by an initial
trend period followed by an equilibrium period. Scientists may wish to quantify
features of the two periods, as well as the timing of the change point.
Specifically, we are motivated by problems in the study of electrical
cell-substrate impedance sensing (ECIS) data. ECIS is a popular new technology
which measures cell behavior non-invasively. Previous studies using ECIS data
have found that different cell types can be classified by their equilibrium
behavior. However, it can be challenging to identify when equilibrium has been
reached, and to quantify the relevant features of cells' equilibrium behavior.
In this paper, we assume that measurements during the trend period are
independent deviations from a smooth nonlinear function of time, and that
measurements during the equilibrium period are characterized by a simple long
memory model. We propose a method to simultaneously estimate the parameters of
the trend and equilibrium processes and locate the change point between the
two. We find that this method performs well in simulations and in practice.
When applied to ECIS data, it produces estimates of change points and measures
of cell equilibrium behavior which offer improved classification of infected
and uninfected cells.
