Bias Contributions in Time Series Models for Resampled Irregular Data

Slotted resampling transforms an irregularly sampled process into an equidistantly resampled signal where data are missing. This always causes bias in spectral estimates, due to aliasing in the frequency domain and to shifting the observation times to an equidistant grid. Furthermore, too low order models can cause a significant truncation bias and probably missing-data bias, both of which disappear if the model orders are taken high enough. The aliasing bias is reduced if a higher resampling frequency is used. Finally, the shift bias can be diminished by using a slot width that is smaller than the resampling time step. An approximate maximum likelihood time series estimator has been developed to estimate the power spectral density and the autocorrelation function of multi-shift slotted nearest neighbor resampled data sets. The bias is independent of the sample size and will not diminish if more data can be used for the estimation. Estimated spectra of irregular observations converge to the aliased biased spectrum for increasing sample sizes. Therefore, accurate spectra require a small bias.