Time Series Decomposition into Oscillation Components and Phase Estimation.

Area of Science:

• Time Series Analysis
• Signal Processing
• Computational Neuroscience

Background:

• Time series often comprise multiple superimposed oscillation components, crucial in fields like neuroscience (e.g., EEG alpha, beta, gamma waves).
• Accurate decomposition and phase analysis of these oscillations are vital for understanding underlying processes.

Purpose of the Study:

• To develop a data-driven method for decomposing time series into constituent oscillation components using state-space models.
• To enable accurate estimation of oscillation phases and amplitudes, facilitating the study of time series phase dynamics.
• To determine the optimal number of oscillation components automatically.

Main Methods:

• Utilized Gaussian linear state-space models with random frequency modulation to represent oscillation components.
• Employed empirical Bayes methods for data-driven estimation of model parameters (amplitudes, frequencies).
• Applied the Akaike Information Criterion (AIC) to select the appropriate number of oscillation components.

Main Results:

• Successfully decomposed time series into natural oscillation components, determining amplitudes and frequencies from data.
• Demonstrated the method's ability to extract intermittent oscillations (e.g., ripples) and detect phase reset phenomena.
• Showcased applicability across diverse fields including astronomy, ecology, tidology, and neuroscience.

Conclusions:

• The proposed state-space modeling approach offers a robust and data-driven method for time series decomposition into oscillations.
• This method provides advantages over traditional techniques like the Hilbert transform for phase estimation in neural time series.
• The technique facilitates deeper insights into the phase dynamics of complex time series across various scientific disciplines.