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arXiv · 1802.09053

Estimation of the Evolutionary Spectra with Application to Stationarity Test

Yu Xiang·Jie Ding·Vahid Tarokh
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Abstract

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.

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Yu Xiang, Jie Ding, Vahid Tarokh. 2018-02-25. Estimation of the Evolutionary Spectra with Application to Stationarity Test. https://doi.org/10.1109/tsp.2018.2890369

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