Fourier spectral factor model for prediction of multidimensional signals

A prediction model for multidimensional weakly stationary signals positing fewer number of common dynamic unobserved factors than the number of measured signals is presented. The strategy involves decomposing the measured signals into two independent parts such that one of them is multidimensional idiosyncratic noise while the other is enforced to bear the dynamic covariances using an appropriately transformed lower dimensional factor. The autocovariance functions of the two components are estimated using a Fourier spectral factor model – Spector – by the principle of maximum likelihood. Using the asymptotic properties of discrete Fourier transform, an estimation method based on eigenvalue decomposition of the spectral density function is presented. The predictability using Spector is validated by vector autoregression on publicly available database of signals.