Frequency identification in Singular Spectrum Analysis

Music City Center 

The decomposition of time series into their fundamental components is a key problem in many disciplines. Singular Spectrum Analysis (SSA) is a nonparametric method for time series modeling and forecasting. By applying Singular Value Decomposition (SVD) to the trajectory matrix-or equivalently, by diagonalizing the second-moment matrix-SSA extracts quasi-orthogonal components that maximize variability. These components provide natural estimates of the underlying trend, cycles, and noise in the original time series. However, standard SSA does not explicitly associate these components with specific oscillation frequencies.
We introduce a novel extension of SSA that simultaneously achieves frequency identification and variance diagonalization. As a byproduct, our approach also yields a consistent estimator of the spectral density. We illustrate the performance of the method through simulations and apply it to various real-world datasets including paleoclimate temperature records and Gross Domestic Product data from multiple countries. In the latter application, we disentangle common from idiosyncratic fluctuations per frequency in international business cycles.

signal extraction

time series

singular spectrum analysis

cycles

frequency identification

eigenvalues 

Business and Economic Statistics Section