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The zero‐crossing rate of p th‐order autoregressive processes
Author(s) -
Cheng Ximing,
Wu Yougui,
Du Jinguan,
Liu Huowang
Publication year - 1997
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00055
Subject(s) - autoregressive model , mathematics , zero (linguistics) , rate of convergence , statistics , unit root , convergence (economics) , philosophy , linguistics , channel (broadcasting) , economic growth , electrical engineering , economics , engineering
He and Kedem have studied the relationship between the zero‐ crossing rate (ZCR) of a second‐o rder autoregressive process and its characteristic roots and have found that, when the roots are on the unit circle, the ZCR converges in mean square to θ/π very quickly regardless of the noise level. In this paper, the ZCR of a p th‐order autoregressive process ((AR) p ) is investigated. The relationships betwe en the ZCR and the one‐step asymptotic correlation function (ACF) and between the one‐step ACF and the characteristic roots of the AR( p ) model are discussed, and some links between the convergence rate of the ZCR and the characte ristic roots are considered.