Bias-Free Estimation of the Auto- and Cross-Covariance and the Corresponding Power Spectral Densities from Gappy Data

04/27/2023

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Signal processing of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Besides randomly and independently occurring outliers also correlated data gaps are investigated. Non-parametric estimators for the mean value, the signal variance, the autocovariance and cross-covariance functions and the corresponding power spectral densities are given, which are bias-free, independent of the spectral composition of the data gaps. Bias-free estimation is obtained by averaging over valid samples only from the data set. The procedures abstain from interpolation of missing samples. An appropriate bias correction is used for cases where the estimated mean value is subtracted out from the data. Spectral estimates are obtained from covariance functions using Wiener-Khinchin's theorem.

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Bias-Free Estimation of the Auto- and Cross-Covariance and the Corresponding Power Spectral Densities from Gappy Data

Practical Realization of Bessel's Correction for a Bias-Free Estimation of the Auto-Covariance and the Cross-Covariance Functions

Interpolation problem for periodically correlated stochastic sequences with missing observations

Estimation problem for continuous time stochastic processes with periodically correlated increments

Filtering of Multidimensional Stationary Sequences with Missing Observations

Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise

Minimax extrapolation problem for periodically correlated stochastic sequences with missing observations

Filtering problem for sequences with periodically stationary multiseasonal increments with spectral densities allowing canonical factorizations

Bias-Free Estimation of the Auto- and Cross-Covariance and the Corresponding Power Spectral Densities from Gappy Data

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Practical Realization of Bessel's Correction for a Bias-Free Estimation of the Auto-Covariance and the Cross-Covariance Functions

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Estimation problem for continuous time stochastic processes with periodically correlated increments

Filtering of Multidimensional Stationary Sequences with Missing Observations

Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise

Minimax extrapolation problem for periodically correlated stochastic sequences with missing observations

Filtering problem for sequences with periodically stationary multiseasonal increments with spectral densities allowing canonical factorizations