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

We consider the problem of testing whether the observations X 1; . . . ;X n 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 see front matter r 2005 Elsevier B.V. All rights reserved. .jeconom.2005.01.034 nding author. Tel.: +1514 343 2400; fax: +1 514 343 5831. dresses: [email protected] (J.-M. Dufour), [email protected] [email protected] (M. Hallin). p://www.fas.umontreal.ca/SCECO/Dufour. Research Chair in Econometrics, CIRANO, CIREQ, and Département de sciences , Université de Montréal.