Math @ Duke
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Publications [#341252] of Vahid Tarokh
Papers Published
- Xiang, Y; Ding, J; Tarokh, V, Estimation of the evolutionary spectra with application to stationarity test,
Ieee Transactions on Signal Processing, vol. 67 no. 5
(March, 2019),
pp. 1353-1365, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC [doi]
(last updated on 2023/06/01)
Abstract: In this paper, 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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