A Nonparametric Test for Weak Dependence Against Strong Cycles and its Bootstrap Analogue
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. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.
Year of publication: |
2007
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Authors: | Hidalgo, Javier |
Published in: |
Journal of Time Series Analysis. - Wiley Blackwell, ISSN 0143-9782. - Vol. 28.2007, 3, p. 307-349
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Publisher: |
Wiley Blackwell |
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