  The orientational memory of particles can serve as an effective measure of
diffusivity, spreading, and search efficiency in complex stochastic processes.
We develop a theoretical framework to describe the decay of directional
correlations in a generic class of stochastic active processes consisting of
distinct states of motion characterized by their persistence and switching
probabilities between the states. For exponentially distributed sojourn times,
the orientation autocorrelation is analytically derived and the characteristic
times of its crossovers are obtained in terms of the persistence of each state
and the switching probabilities. We show how non-exponential sojourn-time
distributions of interest, such as Gaussian and power-law distributions, can
result from history-dependent transitions between the states. The relaxation
behavior of the correlation function in such non-Markovian processes is
governed by the history-dependence of the switching probabilities and cannot be
solely determined by the mean sojourn times of the states.
