Time series models for spectral analysis of irregular data far beyond the mean data rate

Slotted resampling transforms an irregularly sampled process into an equidistantly sampled signal where data are missing. Equidistant resampling always causes spectral bias, due to aliasing and to shifting of the observation times. The shift bias can be diminished by using a slot width that is smaller than the resampling time step. A special approximate maximum likelihood time series estimator has been developed to estimate the power spectral density and the autocorrelation function of multi-shift slotted nearest-neighbour resampled data sets with missing observations. The algorithm estimates several time series models and selects the best model order and model type from a number of candidates. It is tested with benchmark data. It can estimate spectra up to frequencies more than a thousand times higher than the mean data rate. It can be applied to various irregularly sampled data, including bubbly turbulent flow and very sparse climate or atmospheric data.