  In this work, we propose a new inference procedure for understanding
non-stationary processes, under the framework of evolutionary spectra developed
by Priestley. Among various frameworks of modeling non-stationary processes,
the distinguishing feature of the evolutionary spectra is its focus on the
physical meaning of frequency. The classical estimate of the evolutionary
spectral density is based on a double-window technique consisting of a
short-time Fourier transform and a smoothing. However, smoothing is known to
suffer from the so-called bias leakage problem. By incorporating Thomson's
multitaper method that was originally designed for stationary processes, we
propose an improved estimate of the evolutionary spectral density, and analyze
its bias/variance/resolution tradeoff. As an application of the new estimate,
we further propose a non-parametric rank-based stationarity test, and provide
various experimental studies.
