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A Second Order Cumulant Spectrum Test That a Stochastic Process is Strictly Stationary and a Step Toward a Test for Graph Signal Strict Stationarity

Denisa Roberts and Douglas Patterson
Authors registered in the RePEc Author Service: Melvin J. Hinich

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Abstract: This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window averaged sample estimate of the second order cumulant spectrum to build a test statistic with an asymptotic complex standard normal distribution. We derive the test statistic, study the properties of the test and demonstrate its application using 137Cs gamma ray decay data. Future areas of research include testing for strict stationarity of graph signals, with applications in learning convolutional neural networks on graphs, denoising, and inpainting.

Date: 2018-01, Revised 2020-03
New Economics Papers: this item is included in nep-ecm and nep-ets
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Published in NeurIPS 2018 Workshop for the Spatiotemporal Domain

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Handle: RePEc:arx:papers:1801.06727