Multivariate Time Series Decomposition into Oscillation Components.

Area of Science:

• Time Series Analysis
• Statistical Modeling
• Oscillation Dynamics

Background:

• Many real-world time series exhibit complex behaviors resulting from the superposition of multiple underlying oscillatory components.
• Existing methods primarily focus on univariate time series decomposition, limiting their application to multivariate datasets.

Purpose of the Study:

• To extend a previously developed univariate time series decomposition method to handle multivariate data.
• To develop a data-driven approach for identifying and analyzing the phase dynamics of multiple underlying oscillators in multivariate time series.

Main Methods:

• Development of Gaussian linear state-space models to represent multivariate time series as projections of underlying oscillators.
• Estimation of model parameters using the empirical Bayes method.
• Determination of the optimal number of oscillators via the Akaike Information Criterion (AIC).

Main Results:

• Successful decomposition of multivariate time series into constituent oscillation components.
• Estimation of amplitude and phase modulation for each oscillator across variables.
• Demonstration of the method's effectiveness using numerical simulations and real-world sunspot number data, revealing an interesting phase relationship.

Conclusions:

• The proposed method effectively extracts underlying oscillators from multivariate time series in a data-driven manner.
• The approach enables the investigation of complex phase dynamics within multivariate datasets.
• The findings highlight the utility of the method for analyzing phenomena with coupled oscillatory behaviors, such as solar activity.