Detecting frequency modulation in stochastic time series data

TL;DR

This paper introduces a new statistical test for detecting non-stationary frequency modulation in stochastic time series, using instantaneous phase and surrogate data for reliable identification.

Contribution

The paper presents a novel, interpretable, and computationally efficient method for identifying frequency modulation in stochastic processes without needing hyperparameter tuning.

Findings

Correctly identifies over 99% of non-stationary data with frequency doubling.

Uses surrogate data to derive reliable critical values.

Method is easy to interpret and computationally inexpensive.

Abstract

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.