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.
| Original language | English (US) |
|---|---|
| Article number | 8598905 |
| Pages (from-to) | 1353-1365 |
| Number of pages | 13 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 67 |
| Issue number | 5 |
| DOIs | |
| State | Published - Mar 1 2019 |
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Keywords
- Evolutionary spectra
- Multitaper method
- Non-stationary processes
- Spectral analysis
- Stationarity test
Cite this
Estimation of the evolutionary spectra with application to stationarity test. / Xiang, Yu; Ding, Jie; Tarokh, Vahid.
In: IEEE Transactions on Signal Processing, Vol. 67, No. 5, 8598905, 01.03.2019, p. 1353-1365.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Estimation of the evolutionary spectra with application to stationarity test
AU - Xiang, Yu
AU - Ding, Jie
AU - Tarokh, Vahid
PY - 2019/3/1
Y1 - 2019/3/1
N2 - 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.
AB - 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.
KW - Evolutionary spectra
KW - Multitaper method
KW - Non-stationary processes
KW - Spectral analysis
KW - Stationarity test
UR - http://www.scopus.com/inward/record.url?scp=85060514495&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060514495&partnerID=8YFLogxK
U2 - 10.1109/TSP.2018.2890369
DO - 10.1109/TSP.2018.2890369
M3 - Article
AN - SCOPUS:85060514495
VL - 67
SP - 1353
EP - 1365
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 5
M1 - 8598905
ER -