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RESULTS ON ESTIMATION AND TESTING FOR A UNIT ROOT IN THE NONSTATIONARY AUTOREGRESSIVE MOVING‐AVERAGE MODEL
Author(s) -
Yap Sook Fwe,
Reinsel Gregory 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.tb00238.x
Subject(s) - mathematics , unit root , autoregressive–moving average model , autoregressive model , asymptotic distribution , univariate , statistics , unit root test , statistic , autoregressive integrated moving average , star model , moving average model , likelihood ratio test , test statistic , moving average , statistical hypothesis testing , multivariate statistics , time series , cointegration , estimator
. We review the limiting distribution theory for Gaussian estimation of the univariate autoregressive moving‐average (ARMA) model in the presence of a unit root in the autoregressive (AR) operator, and present the asymptotic distribution of the associated likelihood ratio (LR) test statistic for testing for a unit root in the ARMA model. The finite sample properties of the LR statistic as well as other unit root test procedures for the ARMA model are examined through a limited simulation study. We conclude that, for practical empirical work that relies on standard computations, the LR test procedure generally performs better than other standard procedures in the presence of a substantial moving‐average component in the ARMA model.