Bootstrap Testing for Long Range Dependence

Argjir Butka; Llukan Puka; Ilir Palla

doi:https://doi.org/10.14445/22315373/IJMTT-V8P522

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 8 | Number 2 | Year 2014 | Article Id. IJMTT-V8P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V8P522

Bootstrap Testing for Long Range Dependence

Argjir Butka, Llukan Puka, Ilir Palla

Citation :

Argjir Butka, Llukan Puka, Ilir Palla, "Bootstrap Testing for Long Range Dependence," International Journal of Mathematics Trends and Technology (IJMTT), vol. 8, no. 2, pp. 164-172, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V8P522

Abstract

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.

Keywords

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

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