Improvement of the Likelihood Ratio Test Statistic in ARMA Models

Lagos, Bernardo; Morettin, Pedro A.

doi:10.1111/j.1467-9892.2004.00338.x

Cited by 13 publications

(17 citation statements)

References 32 publications

(38 reference statements)

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“…We observe that this correction also does not depend of the nuisance parameter σ 2 , a situation that was also noticed for the corrections for the likelihood ratio statistic [Lagos and Morettin (2004)]. …”

Section: Applicationssupporting

confidence: 75%

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Some corrections of the score test statistic for Gaussian ARMA models

Lagos¹,

Morettin²,

Barroso³

2010

Braz. J. Probab. Stat.

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In this article we compute three corrected score statistic versions: the Bartlett-type correction and the monotone corrected score statistics proposed by Kakizawa [Biometrika 83 (1996) 923-927] and Cordeiro, Ferrari and Cysneiros [J. Stat. Comput. Simul. 62 (1998) 123-136]. These corrected statistics are used to test the null hypothesis concerning some parameter of interest of an ARMA model, assumed to be Gaussian, stationary and invertible. We also consider the situations where nuisance parameters are present. The formulas are written in matrix form, appropriate for the use of symbolic or numerical languages. Some simulation results are also presented for the AR(1), MA(1) and ARMA(1, 1) models.

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Section: Applicationssupporting

confidence: 75%

“…First we simplify some terms involved in the coefficients A 1 and A 2 given in (2.6) and (2.7), respectively, using the cumulants approximated in terms of the integrals I's provided in Lagos and Morettin (2004). The remaining elements are written using the "exact" cumulants κ's (although in the special models we use the approximations).…”

mentioning

confidence: 99%

Some corrections of the score test statistic for Gaussian ARMA models

Lagos¹,

Morettin²,

Barroso³

2010

Braz. J. Probab. Stat.

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“…Following Lagos and Morettin (2004), the AR(1) and MA(1) models are both used to obtain simulated data from which test statistics are calculated. For these two schemes, Lagos and Morettin report results for tests of the null hypothesis that the parameter equals the value actually used to generate the data (see Lagos and Morettin, 2004, Sec. 5.1, Case A; and Sect.…”

Section: A Simulation Studymentioning

confidence: 99%

“…In the experiments, φ 1 has seven values given by Thus, as in Lagos and Morettin (2004), the AR parameter goes from −0.9 to 0.9 in steps of 0.3. Corresponding to Case A of Subsection 5.1 of Lagos and Morettin (2004, pp. 93–4), the seven pairs of null and alternative hypotheses in this case are given by and…”

Section: A Simulation Studymentioning

confidence: 99%

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Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods

Canepa

Godfrey

2006

Journal Time Series Analysis

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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. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

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Improved likelihood-based inference in Birnbaum–Saunders nonlinear regression models

Lemonte

Cordeiro

Moreno-Arenas

2016

Applied Mathematical Modelling

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We address the issue of performing testing inference in Birnbaum-Saunders nonlinear regression models when the sample size is small. The likelihood ratio, Wald and score statistics provide the basis for testing inference on the parameters in this class of models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test statistics. We derive a general Bartlett-type correction in matrix notation for the score test, which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald and score tests, and with the Bartlett-corrected likelihood ratio test, and bootstrapcorrected tests. Our simulation results suggest that the proposed corrected test can be an interesting alternative to other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.

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Improvement of the Likelihood Ratio Test Statistic in ARMA Models

Cited by 13 publications

References 32 publications

Some corrections of the score test statistic for Gaussian ARMA models

Some corrections of the score test statistic for Gaussian ARMA models

Improvement of the quasi‐likelihood ratio test in ARMA models: some results for bootstrap methods

Improved likelihood-based inference in Birnbaum–Saunders nonlinear regression models

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