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Article

Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals

1
Department of Statistical Science, Southern Methodist University, Dallas, TX 75275, USA
2
School of Biological Sciences, University of California Irvine, Irvine, CA 92697, USA
3
Statistics Program, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(12), 1375; https://doi.org/10.3390/e22121375
Received: 22 October 2020 / Revised: 28 November 2020 / Accepted: 3 December 2020 / Published: 5 December 2020
(This article belongs to the Special Issue Time Series Modelling)
In some applications, it is important to compare the stochastic properties of two multivariate time series that have unequal dimensions. A new method is proposed to compare the spread of spectral information in two multivariate stationary processes with different dimensions. To measure discrepancies, a frequency specific spectral ratio (FS-ratio) statistic is proposed and its asymptotic properties are derived. The FS-ratio is blind to the dimension of the stationary process and captures the proportion of spectral power in various frequency bands. Here we develop a technique to automatically identify frequency bands that carry significant spectral power. We apply our method to track changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. At every epoch (a distinct time segment from the duration of the experiment), the nonstationary LFP signal is decomposed into stationary and nonstationary latent sources and the complexity is analyzed through these latent stationary sources and their dimensions that can change across epochs. The analysis indicates that spectral information in the Beta frequency band (12–30 Hertz) demonstrated the greatest change in structure and complexity due to the stroke. View Full-Text
Keywords: multivariate time series; nonstationary; spectral matrix; local field potential multivariate time series; nonstationary; spectral matrix; local field potential
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MDPI and ACS Style

Sundararajan, R.R.; Frostig, R.; Ombao, H. Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals. Entropy 2020, 22, 1375. https://doi.org/10.3390/e22121375

AMA Style

Sundararajan RR, Frostig R, Ombao H. Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals. Entropy. 2020; 22(12):1375. https://doi.org/10.3390/e22121375

Chicago/Turabian Style

Sundararajan, Raanju R., Ron Frostig, and Hernando Ombao. 2020. "Modeling Spectral Properties in Stationary Processes of Varying Dimensions with Applications to Brain Local Field Potential Signals" Entropy 22, no. 12: 1375. https://doi.org/10.3390/e22121375

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