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Tests of Independence in Time Series

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  • R. J. Kulperger
  • R. A. Lockhart

Abstract

Tests of the hypothesis that a seriesX1...,Xn is a sequence of independent and identically distributed observations are investigated. The tests are based on a smoothing of the plotXi+1 againstXi. Asymptotic distribution theory on the null hypothesis and under contiguous alternatives is derived. The resulting limit distributions are available in published tables. Omnibus quadratic statistics of the Anderson–Darling type are compared with some optimal statistics and are shown to have good asymptotic properties. A Monte Carlo study is provided to show that the tests have good small sample properties

Suggested Citation

  • R. J. Kulperger & R. A. Lockhart, 1998. "Tests of Independence in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 165-185, March.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:2:p:165-185
    DOI: 10.1111/1467-9892.00084
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    Cited by:

    1. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.

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