Wavelet variances and covariances (sometime also known as wavelet spectra and co-spectra) are a form of analysis of variance that find
extensive use in the study of time series arising from atmospheric science, economics, hydrology, oceanography, soil science and other
areas of geophysics. Specifically, as precursor to a more formal statistical analysis, wavelet variances and covariances are often applied
to time series to explore their structure and behavior, to identify important scales, to assess long memory parameters, to detect
inhomogeneity and to estimate time-varying spectral densities. In this talk, we focus on estimation and inference of wavelet variances
and covariances when the observed time series is gappy, i.e., sampled at regular intervals, but certain observations are missing.
In particular, we propose a method of estimation that extends the usual estimation procedure for the non-gappy data, investigate statistical
properties and discuss large sample theory. We then show how our approach to this problem opens up new avenues in advancing statistical
calculations for wavelet-based principal components, clustering and classification of multivariate time series that contain missing values.
Finally, we consider an application of our method to NOAA's tropical sea level barometric pressure data.This is joint work with Don Percival,
University of Washington.