Bootstrap Testing for Long Range Dependence

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2014 by IJMTT Journal
Volume-8 Number-3
Year of Publication : 2014
Authors : Argjir Butka , Llukan Puka , Ilir Palla


Argjir Butka , Llukan Puka , Ilir Palla. "Bootstrap Testing for Long Range Dependence", International Journal of Mathematical Trends and Technology (IJMTT). V8:164-172 April 2014. ISSN:2231-5373. Published by Seventh Sense Research Group.

The presence of long-memory or long-range dependence (LRD) in a stochastic process has important consequences in statistical inferences. Lo develops a robust test for detecting the existence of LRD and derives its asymptotic distribution. Teverovsky et al. uncover some drawbacks to using Lo’s method in practice. In particular, they find that Lo’s method has a strong preference for accepting the null hypothesis of no LRD. The bootstrap provides a practical method to correct the size distortion of the asymptotic tests. In this paper, we introduce a semi-parametric bootstrap testing procedure for detecting LRD. We investigate the size and power of Lo’s and its bootstrap tests by means of a computer simulation study. The results suggest that the bootstrap tests correct for size distortions of asymptotic tests for small sample sizes.


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Long-range dependence, fractional differencing, modified R/S statistic, block bootstrap, cycling blocks.