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Some robust exact results on sample autocorrelations and tests of randomness

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  • Dufour, Jean-Marie
  • Roy, Roch

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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 29 (1985)
Issue (Month): 3 (September)
Pages: 257-273

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Handle: RePEc:eee:econom:v:29:y:1985:i:3:p:257-273

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Web page: http://www.elsevier.com/locate/jeconom

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Cited by:
  1. Andrew W. Lo & A. Craig MacKinlay, 1988. "The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation," NBER Technical Working Papers 0066, National Bureau of Economic Research, Inc.
  2. 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.
  3. 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.
  4. Marc Hallin & Abdeljelil Farhat & Jean-Marie Dufour, 2006. "Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series," ULB Institutional Repository 2013/2143, ULB -- Universite Libre de Bruxelles.
  5. 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.
  6. Kan, Raymond & Wang, Xiaolu, 2010. "On the distribution of the sample autocorrelation coefficients," Journal of Econometrics, Elsevier, vol. 154(2), pages 101-121, February.
  7. Coenen, Günter, 2000. "Asymptotic confidence bands for the estimated autocovariance and autocorrelation functions of vector autoregressive models," Working Paper Series 0009, European Central Bank.
  8. 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.
  9. Richard Luger, 2004. "Exact Permutation Tests for Non-nested Non-linear Regression Models," Emory Economics 0419, Department of Economics, Emory University (Atlanta).
  10. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
  11. 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.
  12. Kheoh, Thian S. & McLeod, A. Ian, 1992. "Comparison of two modified portmanteau tests for model adequacy," Computational Statistics & Data Analysis, Elsevier, vol. 14(1), pages 99-106, June.
  13. 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.

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