Premium
THE ZERO‐CROSSING RATE OF AUTOREGRESSIVE PROCESSES AND ITS LINK TO UNIT ROOTS
Author(s) -
He Shuyuan,
Kedem Benjamin
Publication year - 1990
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/j.1467-9892.1990.tb00052.x
Subject(s) - mathematics , autoregressive model , unit root , zero (linguistics) , rate of convergence , polynomial , statistics , unit circle , unit (ring theory) , zero crossing , convergence (economics) , mathematical analysis , key (lock) , ecology , philosophy , mathematics education , quantum mechanics , voltage , economics , biology , economic growth , linguistics , physics
. The asymptotic zero‐crossing rate (ZCR) of the general second‐order autoregressive process is investigated. When the associated characteristic polynomial has a unit root e iθ (0 ≤θ≤π), the ZCR converges in mean square to θ/π and the rate of convergence is very fast regardless of the noise level.