IDEAS home Printed from https://ideas.repec.org/p/cmf/wpaper/wp2021_2103.html
   My bibliography  Save this paper

Multivariate Hermite polynomials and information matrix tests

Author

Listed:

Abstract

We show that the information matrix test for a multivariate normal random vector coincides with the sum of the two moment tests that look at the means of all the different third- and fourth-order multivariate Hermite polynomials, respectively. We also explain how to simulate its exact, parameter-free, finite sample distribution to any desired degree of accuracy for any dimension of the random vector and sample size. Specifically, we exploit the numerical invariance of the test statistic to affine transformations of the observed variables to simulate draws extremely quickly.

Suggested Citation

  • Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2021. "Multivariate Hermite polynomials and information matrix tests," Working Papers wp2021_2103, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2021_2103
    as

    Download full text from publisher

    File URL: https://www.cemfi.es/ftp/wp/2103.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
    2. Kiefer, Nicholas M. & Salmon, Mark, 1983. "Testing normality in econometric models," Economics Letters, Elsevier, vol. 11(1-2), pages 123-127.
    3. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    4. J. Koziol, 1987. "An alternative formulation of Neyman’s smooth goodness of fit tests under composite alternatives," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 34(1), pages 17-24, December.
    5. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    6. Best, D. J. & Rayner, J. C. W., 1988. "A test for bivariate normality," Statistics & Probability Letters, Elsevier, vol. 6(6), pages 407-412, May.
    7. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    8. Pietro BALESTRA & Alberto HOLLY, 1990. "A General Kronecker Formula for the Moments of the Multivariate Normal Distribution," Cahiers de Recherches Economiques du Département d'économie 9002, Université de Lausanne, Faculté des HEC, Département d’économie.
    9. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
    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. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Tests for Random Coefficient Variation in Vector Autoregressive Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 1-35, Emerald Group Publishing Limited.

    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. Jinghui Chen & Masahito Kobayashi & Michael McAleer, 2017. "Testing for volatility co-movement in bivariate stochastic volatility models," Documentos de Trabajo del ICAE 2017-10, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    2. Jinghui Chen & Masahito Kobayashi & Michael McAleer, 2016. "Testing for a Common Volatility Process and Information Spillovers in Bivariate Financial Time Series Models," Documentos de Trabajo del ICAE 2016-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Loperfido, Nicola, 2020. "Some remarks on Koziol’s kurtosis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    4. Dante Amengual & Xinyue Bei & Enrique Sentana, 2022. "Normal but skewed?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1295-1313, November.
    5. Apostolos Serletis & Ricardo Rangel-Ruiz, 2007. "Testing for Common Features in North American Energy Markets," World Scientific Book Chapters, in: Quantitative And Empirical Analysis Of Energy Markets, chapter 14, pages 172-187, World Scientific Publishing Co. Pte. Ltd..
    6. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    7. Mamingi Nlandu, 2017. "Beauty and Ugliness of Aggregation over Time: A Survey," Review of Economics, De Gruyter, vol. 68(3), pages 205-227, December.
    8. Osmani Teixeira de Carvalho de Guillén & Carlos Hamilton Vasconcelos Araújo, 2005. "O Mecanismo De Transmissão Da Taxa De Câmbio Para Índices De Preços: Uma Análise Vecm Para O Brasil," Anais do XXXIII Encontro Nacional de Economia [Proceedings of the 33rd Brazilian Economics Meeting] 034, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    9. Lafuente, Juan A. & Novales, Alfonso, 2003. "Optimal hedging under departures from the cost-of-carry valuation: Evidence from the Spanish stock index futures market," Journal of Banking & Finance, Elsevier, vol. 27(6), pages 1053-1078, June.
    10. Gaia Garino & Lucio Sarno, 2004. "Speculative Bubbles in U.K. House Prices: Some New Evidence," Southern Economic Journal, John Wiley & Sons, vol. 70(4), pages 777-795, April.
    11. Chen, Xiaoshan & Mills, Terence C., 2009. "Evaluating growth cycle synchronisation in the EU," Economic Modelling, Elsevier, vol. 26(2), pages 342-351, March.
    12. Sharon Kozicki & Peter A. Tinsley, "undated". "Moving Endpoints in Macrofinance," Computing in Economics and Finance 1996 _058, Society for Computational Economics.
    13. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    14. Harvey, David I. & Mills, Terence C., 2002. "Common features in UK sectoral output," Economic Modelling, Elsevier, vol. 19(1), pages 91-104, January.
    15. Michael J. Artis, 2002. "Reflections on the Optimal Currency Area (OCA) criteria in the light of EMU," Working Papers 69, Oesterreichische Nationalbank (Austrian Central Bank).
    16. Bergman, Michael, 2001. "Finnish and Swedish Business Cycles in a Global Context," Working Papers 2001:20, Lund University, Department of Economics.
    17. Kapetanios, G. & Pagan, A. & Scott, A., 2007. "Making a match: Combining theory and evidence in policy-oriented macroeconomic modeling," Journal of Econometrics, Elsevier, vol. 136(2), pages 565-594, February.
    18. Fiona Atkins, 2005. "Financial Crises and Money Demand in Jamaica," Birkbeck Working Papers in Economics and Finance 0512, Birkbeck, Department of Economics, Mathematics & Statistics.
    19. David McMillan & Isabel Ruiz & Alan Speight, 2010. "Correlations and spillovers among three euro rates: evidence using realised variance," The European Journal of Finance, Taylor & Francis Journals, vol. 16(8), pages 753-767.
    20. Kozicki, Sharon & Tinsley, P. A., 2001. "Shifting endpoints in the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 613-652, June.

    More about this item

    Keywords

    Exact test; Hessian matrix; multivariate normality; outer product of the score.;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cmf:wpaper:wp2021_2103. 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: Araceli Requerey (email available below). General contact details of provider: https://edirc.repec.org/data/cemfies.html .

    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.