  We propose a new model-free method to detect change points between distinct
phases in a single random trajectory of an intermittent stochastic process. The
local convex hull (LCH) is constructed for each trajectory point, while its
geometric properties (e.g., the diameter or the volume) are used as
discriminators between phases. The efficiency of the LCH method is validated
for six models of intermittent motion, including Brownian motion with different
diffusivities or drifts, fractional Brownian motion with different Hurst
exponents, and surface-mediated diffusion. We discuss potential applications of
the method for detection of active and passive phases in the intracellular
transport, temporal trapping or binding of diffusing molecules, alternating
bulk and surface diffusion, run and tumble (or search) phases in the motion of
bacteria and foraging animals, and instantaneous firing rates in neurons.
