Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

Jean-Marie Dufour (jean-marie.dufour@mcgill.ca), Abdeljelil Farhat (abdeljelil.farhat@umontreal.ca) and Marc Hallin

CIRANO Working Papers from CIRANO

Abstract: We consider the problem of testing whether the observations X1, · · ·, Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate). Nous étudions le problème qui consiste à tester l'hypothèse que des observations X1, · · ·, Xn d'une série chronologique sont indépendantes avec des distributions non spécifiées (possiblement non identiques) symétriques autour d'une médiane connue. Nous proposons plusieurs bornes sur les distributions des coefficients d'autocorrélation : bornes exponen-tielles, bornes de type Eaton, bornes de Chebyshev et bornes de Berry-Esséen-Zolotarev. Les bornes sont exactes dans les échantillons finis, non paramétriques et faciles à calculer. Nous évaluons par simulation la performance des bornes et comparons celle-ci à celle de tests d'autocorrélation traditionnels. Les procédures proposées sont appliquées à des données de taux d'intérêt américaines (commercial paper rate).

Keywords: autocorrelation; serial dependence; nonparametric test; distribution-free test; heterogeneity; heteroskedasticity; symmetric distribution; robustness; exact test; bound; exponential bound; large deviations; Chebyshev inequality; Berry-Esséen; interest rates, autocorrelation; serial dependence; nonparametric test; distribution-free test; heterogeneity; heteroskedasticity; symmetric distribution; robustness; exact test; bound; exponential bound; large deviations; Chebyshev inequality; Berry-Esséen; interest rates (search for similar items in EconPapers)
JEL-codes: C12 C14 C22 C32 E4 (search for similar items in EconPapers)
Date: 2005-02-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mac
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https://cirano.qc.ca/files/publications/2005s-04.pdf

Related works:
Journal Article: Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series (2006)
Working Paper: Distribution-free bounds for serial correlation coefficients in heteroskedastic symmetric time series (2006)
Working Paper: Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series (2005)
Working Paper: Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series (2005)
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