Five Separate Bias Contributions in Time Series Models for Equidistantly Resampled Irregular Data

Abstract—The use of time series models for irregular data requires resampling of the data on an equidistant grid. Slotted resampling transforms an irregular randomly sampled process into an equidistant signal where data are missing. An approximate maximum-likelihood time series estimator has been developed to estimate the power spectral density and the autocorrelation function of multishift slotted nearest-neighbor (NN) resampled data sets. Resampling always causes bias in spectral estimates due to aliasing in the frequency domain and to shifting the observation times to an equidistant grid. Furthermore, orders of the time series models that are too low can cause a significant truncation bias and, probably, an additional missing-data bias, both of which disappear if the model orders are taken high enough. Finally, a special bias is present if the probability of making an observation at a certain time depends on the instantaneous amplitude of the observed signal. All five bias types are independent of the sample size and will not diminish if more data can be used for the estimation. Index Terms—Autoregressive (AR) models, nearest-neighbor (NN) resampling, slotting, spectral analysis, time series, uneven sampling. I