A spectrum Separation Method for the Sum of Two Non-Gaussian Stationary Time Series Using Higher Order Periodograms

When we observe only the sum of two independent stationary time series generated from non-Gaussian white noises, we consider how to separate its spectrum nonparametrically into two respective spectra. For this we propose a simple method which utilizes the nonnegativity of power spectra and uses a part of the fourth-order spectrum estimated from the periodograms. Theoretically, the spectrum is uniquely separated when the spectra of the two time series have different zeros. The simulation results show that our method is successful. The asymptotic property of the method is also investigated.