Simulation Methodology for Inference on Physical Parameters of Complex Vector-Valued Signals

Complex-valued vector time series occur in diverse fields such as oceanography and meteorology, and scientifically interpretable parameters may be estimated from them. We show that it is possible to make inference such as confidence intervals on these parameters using a vector-valued circulant embedding simulation method, combined with bootstrapping. We apply the methodology to three parameters of interest in oceanography, and compare the resulting simulated confidence intervals with those computed using analytic results. We conclude that the simulation scheme offers an inference approach either in the absence of theoretical distributional results, or to check the effect of nuisance parameters where theoretical results are available.