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Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods
Author(s) -
Canepa A.,
Godfrey L. G.
Publication year - 2007
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.1467-9892.2006.00518.x
Subject(s) - mathematics , statistics , independent and identically distributed random variables , autoregressive model , invertible matrix , autoregressive–moving average model , white noise , likelihood ratio test , test statistic , statistic , ratio test , statistical hypothesis testing , econometrics , random variable , pure mathematics
. Quasi‐likelihood ratio tests for autoregressive moving‐average (ARMA) models are examined. The ARMA models are stationary and invertible with white‐noise terms that are not restricted to be normally distributed. The white‐noise terms are instead subject to the weaker assumption that they are independently and identically distributed with an unspecified distribution. Bootstrap methods are used to improve control of the finite sample significance levels. The bootstrap is used in two ways: first, to approximate a Bartlett‐type correction; and second, to estimate the p ‐value of the observed test statistic. Some simulation evidence is provided. The bootstrap p ‐value test emerges as the best performer in terms of controlling significance levels.