  We propose a new statistical test to identify non-stationary
frequency-modulated stochastic processes from time series data. Our method uses
the instantaneous phase as a discriminatory statistics with reliable critical
values derived from surrogate data. We simulated an oscillatory second-order
autoregressive process to evaluate the size and power of the test. We found
that the test we propose is able to correctly identify more than 99% of
non-stationary data when the frequency of simulated data is doubled after the
first half of the time series. Our method is easily interpretable,
computationally cheap and does not require choosing hyperparameters that are
dependent on the data.
