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Some Robust Exact Results on Sample Autocorrelations and Tests of Randomness

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  • Dufour, J.M.
  • Roy, R.

Abstract

Ce Texte Presente Plusieurs Resultats Exacts Sur les Seconds Moments des Autocorrelations Echantillonnales, Pour des Series Gaussiennes Ou Non-Gaussiennes. Nous Donnons D'abord des Formules Generales Pour la Moyenne, la Variance et les Covariances des Autocorrelations Echantillonnales, Dans le Cas Ou les Variables de la Serie Sont Interchangeables. Nous Deduisons de Celles-Ci des Bornes Pour les Variances et les Covariances des Autocorrelations Echantillonnales. Ces Bornes Sont Utilisees Pour Obtenir des Limites Exactes Sur les Points Critiques Lorsqu'on Teste le Caractere Aleatoire D'une Serie Chronologique, Sans Qu'aucune Hypothese Soit Necessaire Sur la Forme de la Distribution Sous-Jacente. Nous Donnons des Formules Exactes et Explicites Pour les Variances et Covariances des Autocorrelations Dans le Cas Ou la Serie Est un Bruit Blanc Gaussien. Nous Montrons Que Ces Resultats Sont Aussi Valides Lorsque la Distribution de la Serie Est Spheriquement Symetrique. Nous Presentons les Resultats D'une Simulation Qui Indiquent Clairement Qu'on Approxime Beaucoup Mieux la Distribution des Autocorrelations Echantillonnales En Normalisant Celles-Ci Avec la Moyenne et la Variance Exactes et En Utilisant la Loi N(0,1) Asymptotique, Plutot Qu'en Employant les Seconds Moments Approximatifs Couramment En Usage. Nous Etudions Aussi les Variances et Covariances Exactes D'autocorrelations Basees Sur les Rangs des Observations.

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 8412.

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Length: 26P. pages
Date of creation: 1984
Date of revision:
Handle: RePEc:mtl:montde:8412

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Keywords: Correlation Analysis ; Econometrie;

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Cited by:
  1. Sneek, J.M. & Smits, J., 1990. "An approximation to the distribution of quadratic forms in many normal variables," Serie Research Memoranda 0049, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  2. Luger, Richard, 2006. "Exact permutation tests for non-nested non-linear regression models," Journal of Econometrics, Elsevier, vol. 133(2), pages 513-529, August.
  3. Lo, Andrew W. & MacKinlay, A. Craig, 1989. "The size and power of the variance ratio test in finite samples : A Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 40(2), pages 203-238, February.
  4. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
  5. Coenen, Günter, 2000. "Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models," Working Paper Series 0009, European Central Bank.
  6. Andy Kwan & Ah-Boon Sim & Yangru Wu, 2005. "On the size and power of normalized autocorrelation coefficients," Applied Financial Economics, Taylor & Francis Journals, vol. 15(1), pages 1-11.
  7. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & HALLIN, Marc, 2005. "Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series," Cahiers de recherche 05-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Kan, Raymond & Wang, Xiaolu, 2010. "On the distribution of the sample autocorrelation coefficients," Journal of Econometrics, Elsevier, vol. 154(2), pages 101-121, February.
  9. Genton, Marc G., 1999. "The correlation structure of the sample autocovariance function for a particular class of time series with elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 131-137, January.
  10. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.
  11. Paolella, Marc S., 2003. "Computing moments of ratios of quadratic forms in normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 313-331, March.
  12. Kwan, Andy C.C. & Sim, Ah-Boon & Wu, Yangru, 2005. "A comparative study of the finite-sample performance of some portmanteau tests for randomness of a time series," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 391-413, February.

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