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ASYMPTOTIC INFERENCE FOR NON‐INVERTIBLE MOVING‐AVERAGE TIME SERIES
Author(s) -
Chan Ngai Hang,
Tsay Ruey S.
Publication year - 1996
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.1467-9892.1996.tb00261.x
Subject(s) - mathematics , autoregressive model , autoregressive–moving average model , invertible matrix , moving average , series (stratigraphy) , asymptotic distribution , stochastic process , statistics , pure mathematics , estimator , paleontology , biology
. This paper is concerned with statistical inference of nonstationary and non‐invertible autoregressive moving‐average (ARMA) processes. It makes use of the fact that a derived process of an ARMA( p, q ) model follows an AR( q ) model with an autoregressive (AR) operator equivalent to the moving‐average (MA) part of the original ARMA model. Asymptotic distributions of least squares estimates of MA parameters based on a constructed derived process are obtained as corresponding analogs of a nonstationary AR process. Extensions to the nearly non‐invertible models are considered and the limiting distributions are obtained as functionals of stochastic integrals of Brownian motions and Ornstein‐Uhlenbeck processes. For application, a two‐stage procedure is proposed for testing unit roots in the MA polynomial. Examples are given to illustrate the application.