Modeling (almost) periodic moving average processes using cyclic statistics

Estimating parameters of almost cyclostationary non-Gaussian moving average (MA) processes using noisy output-only data is considered. It is shown that second-order cyclic correlations of the output are generally insufficient in uniquely characterizing almost periodically time-varying MA(q) models, while third-order and higher order cumulants can be used to estimate their model parameters within a scale factor. Both linear and nonlinear identification algorithms for fixed and time-varying order q(t) are presented. Statistical model order determination procedures are also derived. Implementation issues are discussed and resistance to noise is claimed when the signal of interest has cycles distinct from the additive noise. Simulations are performed to verify the theoretical results.