On autocorrelation estimation in mixed-spectrum Gaussian processes
type: Item
instance of: scholarly article
title: On autocorrelation estimation in mixed-spectrum Gaussian processes
zbMATH Open document ID: 0796.62075
DOI: 10.1016/0304-4149(94)90136-8
published in: Stochastic Processes and their Applications
publication date: 1994-10-11T00:00:00Z
review text: Let \(z = \{z_ t\}\), \(t = 0,\pm 1,\dots\) be a real-valued, zero-mean stationary Gaussian process with autocorrelation \(\rho_ z(k)\), and let \(d = \{d_ t\}\) be the associated zero-crossing indicator process. Given \(z_ 1,\dots,z_ N\), the empirical zero-crossing rate is defined as \(\widehat{\gamma} = (\pi/(N - 1))\sum^ N_{t = 2} d_ t\). Then \(\rho_ z(1) = \cos(E(\widehat{\gamma}))\). The paper considers the estimation of \(\rho_ z(1)\), using \(\widehat{\rho}_ z(1) = \cos(\widehat{\gamma})\). It is proved that it is consistent for a spectrum supported at a single frequency, or a spectrum for which the signal and noise have the exact same first-order autocorrelation.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 62M07
zbMATH DE Number: 519769
zbMATH Keywords: spectral atoms
zbMATH Keywords: spectral measure
zbMATH Keywords: ergodic
zbMATH Keywords: Wiener-Ito integrals
zbMATH Keywords: real- valued, zero-mean stationary Gaussian process
zbMATH Keywords: zero-crossing indicator problem
zbMATH Keywords: empirical zero-crossing rate
zbMATH Keywords: first-order autocorrelation
author: Benjamin Kedem-Kimelfeld
author: Eric V. Slud
reviewed by: Pedro A. Morettin
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90136-8
OpenAlex ID: W2083884032
cites work: Q5544740
cites work: Higher order crossings spectral analysis of an almost periodic random sequence in noise
cites work: Estimation of the Parameters in Stationary Autoregressive Processes after Hard Limiting
cites work: A Stochastic Characterization of the Sine Function
cites work: On the asymptotic variance of higher order crossings with special reference to a fast white noise test
cites work: Time series discrimination by higher order crossings
cites work: Q4778193
cites work: Deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes
cites work: Q3227937
cites work: Multiple Wiener-Ito integrals. With applications to limit theorems
cites work: Multiple Wiener-Itô integral expansions for level-crossing-count functionals
cites work: Q3776310
cites work: The effect of a memoryless nonlinearity on the spectrum of a random process
cites work: Correlation theory of stationary and related random functions. Volume I: Basic results
description: scientific article; zbMATH DE number 519769