Time series very rarely are collected without some missing observations. While modeling and inference of missing data time series is often done without much lipservice to the estimation of the covariance of such a sample, it is certain that high-frequency information is lost and under some circumstances is impossible to recover, even when a very small proportion of data is missing. Where there is unequal sampling cadence, even more severe artifacts can be observed, such as the introduction of quasi-alias peaks and high error in certain bands in frequency.

Most importantly, no modeling approach will be able to recover information that isn't contained in the estimated covariance. In this talk, we concern ourselves with estimation of the spectral properties of univariate and multivariate time series, with special attention to the astronomical literature.  We propose the design of optimal tapering (Slepian) sequences which send to zero the missing observations, while simultaneously concentrating power to a delta like function in the spectral domain. These optimal sequences are then premultiplied by the data before estimation of the spectrum or coherence to produce estimates with improved statistical properties. If time allows, we concern ourselves with the more general case of unequal sampling cadence, where optimal tapering functions are frequency dependent.

Zoom Link:  https://argonne.zoomgov.com/j/1619753015

See all upcoming talks at http://wordpress.cels.anl.gov/lans-seminars/