  The analysis of nonstationary time series is of great importance in many
scientific fields such as physics and neuroscience. In recent years, Gaussian
process regression has attracted substantial attention as a robust and powerful
method for analyzing time series. In this paper, we introduce a new framework
for analyzing nonstationary time series using locally stationary Gaussian
process analysis with parameters that are coupled through a hidden Markov
model. The main advantage of this framework is that arbitrary complex
nonstationary covariance functions can be obtained by combining simpler
stationary building blocks whose hidden parameters can be estimated in
closed-form. We demonstrate the flexibility of the method by analyzing two
examples of synthetic nonstationary signals: oscillations with time varying
frequency and time series with two dynamical states. Finally, we report an
example application on real magnetoencephalographic measurements of brain
activity.
