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AN APPLICATION OF THE SCHUR‐COHN ALGORITHM TO TIME SERIES ANALYSIS
Author(s) -
Barnard Roger W.,
Chanda Kamal C.
Publication year - 1995
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.1467-9892.1995.tb00245.x
Subject(s) - mathematics , autoregressive–moving average model , autoregressive model , bounded function , series (stratigraphy) , algorithm , matrix (chemical analysis) , set (abstract data type) , statistics , mathematical analysis , computer science , paleontology , materials science , biology , composite material , programming language
. Standard least squares analysis of autoregressive moving‐average (ARMA) processes with errors‐in‐variables entails the construction of a new set of parameters which are functions of the original ARMA parameters, and requires that derivatives of these new parameters of order three or less with respect to the ARMA parameters exist and be bounded. The boundedness of these derivatives in turn depends critically on the nonsingularity of a matrix B which is a function of the ARMA parameters via the new parameters in the model. A particular version of the classical Schur–Cohn algorithm enables us to establish this nonsingularity.