Spectral analysis and stationarity tests

This lecture discusses spectral analysis and stationarity tests for time series with missing values. It covers the motivation behind estimating second-order structure in time series, challenges of stationarity assumption, spectral estimation techniques, tests for stationarity, and the development of tools for spectral analysis suitable for nonstationary time series with missing observations. The lecture also explores wavelet lifting schemes, locally stationary wavelet models, wavelet-based models, multiscale transforms for irregular data, lifting schemes in practice, and the lifting periodogram and spectral estimator. Additionally, it presents a simulation study, a test of stationarity, and concludes with remarks on spectral estimates, stationarity tests, and future research directions.