Detecting frequency modulation in stochastic time-series data.

We propose a statistical test to identify nonstationary 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 nonstationary data when the frequency of the 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.