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.