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Improvement of the Likelihood Ratio Test Statistic in ARMA Models

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  • Bernardo M. Lagos
  • Pedro A. Morettin

Abstract

In this paper, we develop a Bartlett correction for the likelihood ratio statistic used to test hypotheses about parameters of a Gaussian stationary and invertible model belonging to the ARMA (autoregressive moving average) family. Alternative hypotheses with and without disturbance parameters are considered. The correction formulae are written in matrix form with the advantage of being easily implemented with the aid of some symbolic or numerical matrix language. Some simulation results are also presented.

Suggested Citation

  • Bernardo M. Lagos & Pedro A. Morettin, 2004. "Improvement of the Likelihood Ratio Test Statistic in ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 83-101, January.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:83-101
    DOI: 10.1111/j.1467-9892.2004.00338.x
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    References listed on IDEAS

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    1. Taniguchi, Masanobu, 1988. "Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 494-511, November.
    2. Jan R. Magnus, 1978. "The moments of products of quadratic forms in normal variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(4), pages 201-210, December.
    3. Nalini Ravishanker & Edward L. Melnick & Chih‐Ling Tsai, 1990. "Differential Geometry Of Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 259-274, May.
    4. Kees Jan van Garderen, 1999. "Exact Geometry of Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 1-21, January.
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    Cited by:

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    2. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.

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