Factor modeling of multivariate time series: A frequency components approach

Abstract

A frequency domain factor model method for multivariate stationary time series is proposed. The dimension reduction framework aims to find a lower-dimensional multivariate stationary factor series. Frequency components of the observed series are assumed to be linearly generated by the corresponding frequency components of a latent factor series using frequency-specific factor loadings matrices. These loadings matrices are then estimated using an eigendecomposition of symmetric non-negative definite matrices involving the real and imaginary parts of the spectral matrix. The factor dimension is estimated using nonparametric bootstrap tests. Consistency results concerning the estimation of eigenvalues, eigenvectors, factor loadings matrices and the factor dimension are provided. The numerical performance of the proposed method is illustrated through simulation examples. An application to modeling resting-state fMRI time series from autism individuals is demonstrated where a frequency-specific factor analysis helps understand functional connectivity.