Premium
A Nonparametric Test for Weak Dependence Against Strong Cycles and its Bootstrap Analogue
Author(s) -
Hidalgo Javier
Publication year - 2007
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2006.00510.x
Subject(s) - mathematics , bootstrapping (finance) , nonparametric statistics , resampling , statistics , context (archaeology) , weak convergence , sampling distribution , gumbel distribution , statistical hypothesis testing , econometrics , extreme value theory , paleontology , computer security , computer science , asset (computer security) , biology
. 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.