We develop unified theory and methodology for the inference of time-varying spectral densities for a general class of non-stationary and nonlinear processes. In particular, simultaneous confidence regions are constructed for the spectral densities on a nearly optimally dense grid of the time-frequency domain. A simulation based method is proposed to implement the simultaneous confidence regions. The simultaneous confidence regions serve as a unified and visually friendly tool for a wide range of problems in time-frequency analysis such as testing for stationarity and time-frequency separability and validation for non-stationary linear models.

Zhou Zhou obtained his Ph.D. in Statistics from the University of Chicago in 2009. He is currently the Associate Professor and Associate Chair for Graduate Studies at the Department of Statistical Sciences, University of Toronto. Zhou's major research interests lie in non-stationary time series analysis, non- and semi- parametric methods, change points analysis and functional and longitudinal data analysis