Detecting frequency modulation in stochastic time-series data.

Area of Science:

• Time-series analysis
• Stochastic processes
• Signal processing

Background:

• Identifying nonstationary processes in time-series data is crucial for accurate modeling.
• Traditional methods may struggle with frequency-modulated signals.
• Stochastic processes with changing frequencies present unique analytical challenges.

Purpose of the Study:

• To introduce a novel statistical test for identifying nonstationary frequency-modulated stochastic processes.
• To provide a reliable method for analyzing time-series data with dynamic frequency characteristics.
• To develop a computationally efficient and interpretable analysis tool.

Main Methods:

• Utilizing instantaneous phase as a discriminatory statistic.
• Deriving critical values from surrogate data for robust hypothesis testing.
• Simulating an oscillatory second-order autoregressive process for validation.

Main Results:

• The proposed statistical test demonstrated high accuracy, correctly identifying over 99% of nonstationary data.
• Performance was validated using simulated data where frequency doubled mid-time series.
• The method proved effective even with significant frequency shifts.

Conclusions:

• The developed statistical test is a powerful tool for detecting nonstationarity in frequency-modulated stochastic processes.
• The method is computationally inexpensive, easily interpretable, and requires no data-dependent hyperparameters.
• This approach offers a significant advancement in time-series analysis for dynamic signals.