Efficient non parametric spectral density estimation with censored observations

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Spectral density estimation is a well-studied problem for the case of directly observed time series. If data are censored then add hoc methods, like ignoring censored observations or treatment them as missing and using imputation, are recommended. This article, for the first time in the literature, presents the theory and methodology of efficient non parametric spectral density estimation for censored time series. Recommended estimator is based on estimation of autocovariances for censored time series which is of interest on its own. Similarly to the case of direct observations, the theory and methodology are first developed for Gaussian time series, and then robustness of the estimator is verified for a larger class of mixing time series. Simulations and practical examples complement the theory.