IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v25y2004i1p83-101.html
   My bibliography  Save this article

Improvement of the Likelihood Ratio Test Statistic in ARMA Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2004.00338.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2004.00338.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Vargas, Tiago M. & Ferrari, Silvia L.P. & Lemonte, Artur J., 2014. "Improved likelihood inference in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 110-124.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. J. Roderick McCrorie, 2021. "Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 244-281, November.
    3. Schott, James R., 2003. "Kronecker product permutation matrices and their application to moment matrices of the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 177-190, October.
    4. Magnus, J.R. & Pesaran, B., 1990. "Evaluation Of Moment Of Quadratic Forms In Normal Variables," Papers 9021, Tilburg - Center for Economic Research.
    5. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.
    6. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    7. Noud P.A. van Giersbergen, 2013. "Bartlett correction in the stable second‐order autoregressive model with intercept and trend," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 482-498, November.
    8. Hashem Pesaran, M. & Yamagata, Takashi, 2008. "Testing slope homogeneity in large panels," Journal of Econometrics, Elsevier, vol. 142(1), pages 50-93, January.
    9. Robinson, Peter M. & Rossi, Francesca, 2015. "Refinements in maximum likelihood inference on spatial autocorrelation in panel data," Journal of Econometrics, Elsevier, vol. 189(2), pages 447-456.
    10. Jacobson, Tor & Larsson, Rolf, 1999. "Bartlett corrections in cointegration testing," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 203-225, August.
    11. Robert Kollmann, 2013. "Tractable latent state filtering for non-linear DSGE models using a second-order Approximation," CAMA Working Papers 2013-29, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. van den Berg, G., 1986. "Small-sample properties of estimators of the autocorrelation coefficient," Other publications TiSEM 03414dd6-10fa-4f48-a742-e, Tilburg University, School of Economics and Management.
    13. van Garderen, Kees Jan & Peter Boswijk, H., 2014. "Bias correcting adjustment coefficients in a cointegrated VAR with known cointegrating vectors," Economics Letters, Elsevier, vol. 122(2), pages 224-228.
    14. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    15. Patrick Marsh, "undated". "Some Geometry for the Maximal Invariant in Linear Regression," Discussion Papers 04/07, Department of Economics, University of York.
    16. Sneek, J.M., 1982. "Some approximations to the exact distribution of sample autocorrelations for autoregressive moving average models," Serie Research Memoranda 0002, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    17. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.
    18. Yong Bao & Aman Ullah, 2009. "Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications," Working Papers 200907, University of California at Riverside, Department of Economics, revised Jun 2009.
    19. Ghazal, G. A., 1996. "Recurrence formula for expectations of products of quadratic forms," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 101-109, April.
    20. Myrsini Katsikatsou & Irini Moustaki, 2016. "Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1046-1068, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:83-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.