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A Nonparametric Test for Weak Dependence Against Strong Cycles and its Bootstrap Analogue

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  • Javier Hidalgo

Abstract

. We examine a test for the hypothesis of weak dependence against strong cyclical components. We show that the limiting distribution of the test is a Gumbel distribution, denoted G(·). However, since G(·) may be a poor approximation to the finite sample distribution, being the rate of the convergence logarithmic [see Hall Journal of Applied Probability (1979), Vol. 16, pp. 433–439], inferences based on G(·) may not be very reliable for moderate sample sizes. On the other hand, in a related context, Hall [Probability Theory and Related Fields (1991), Vol. 89, pp. 447–455] showed that the level of accuracy of the bootstrap is significantly better. For that reason, we describe an approach to bootstrapping the test based on Efron's [Annals of Statistics (1979), Vol. 7, pp. 1–26] resampling scheme of the data. We show that the bootstrap principle is consistent under very mild regularity conditions.

Suggested Citation

  • Javier Hidalgo, 2007. "A Nonparametric Test for Weak Dependence Against Strong Cycles and its Bootstrap Analogue," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 307-349, May.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:307-349
    DOI: 10.1111/j.1467-9892.2006.00510.x
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