Missing-Data Nonparametric Coherency Estimation

Chave recently proposed an estimator for multitaper spectral density where the time series contains missing values. In this article we generalize this technique to a multitaper estimator of coherence and phase and show that one can also obtain bootstrapped confidence intervals. We give two examples. The first is a toy example in which the true coherence is known. In the second example we show that the multitaper missing-data coherence estimator computed on real data with a single gap comprising 11% of the data outperforms the Daniell-smoothed coherence estimator where there are no gaps. The case where the two time series have different missing indices is also discussed.

Automated summary

This article generalizes Chave's estimator for multitaper spectral density to coherence and phase estimation, with the addition of bootstrapped confidence intervals. Two examples are provided, demonstrating the improved performance of the missing-data coherence estimator over the Daniell-smoothed coherence estimator in real data with gaps. The case of two time series with different missing indices is also discussed.