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

Javier Hidalgo

Journal of Time Series Analysis, 2007, vol. 28, issue 3, 307-349

Abstract: 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.

Date: 2007
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