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HAC estimation and strong linearity testing in weak ARMA models

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  • Francq, Christian
  • Zakoïan, Jean-Michel

Abstract

In the framework of ARMA models, we consider testing the reliability of the standard asymptotic covariance matrix (ACM) of the least-squares estimator. The standard formula for this ACM is derived under the assumption that the errors are independent and identically distributed, and is in general invalid when the errors are only uncorrelated. The test statistic is based on the difference between a conventional estimator of the ACM of the least-squares estimator of the ARMA coefficients and its robust HAC-type version. The asymptotic distribution of the HAC estimator is established under the null hypothesis of independence, and under a large class of alternatives. The asymptotic distribution of the proposed statistic is shown to be a standard [chi]2 under the null, and a noncentral [chi]2 under the alternatives. The choice of the HAC estimator is discussed through asymptotic power comparisons. The finite sample properties of the test are analyzed via Monte Carlo simulation.

Suggested Citation

  • Francq, Christian & Zakoïan, Jean-Michel, 2007. "HAC estimation and strong linearity testing in weak ARMA models," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 114-144, January.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:114-144
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    2. Hecq Alain & Palm Franz C. & Laurent Sébastien, 2016. "On the Univariate Representation of BEKK Models with Common Factors," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 91-113, July.
    3. Hecq Alain & Laurent Sébastien & Palm Franz, 2011. "On the Univariate Representation of Multivariate Volatility Models with Common Factors," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Boubacar Mainassara, Yacouba, 2010. "Selection of weak VARMA models by modified Akaike's information criteria," MPRA Paper 24981, University Library of Munich, Germany.
    5. Boubacar Mainassara, Yacouba, 2010. "Selection of weak VARMA models by Akaïke's information criteria," MPRA Paper 23412, University Library of Munich, Germany.
    6. Boubacar Maïnassara, Yacouba & Raïssi, Hamdi, 2015. "Semi-strong linearity testing in linear models with dependent but uncorrelated errors," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 110-115.
    7. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    8. Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.

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