A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤ^d-actions

2016/11/27 by Ayan Bhattacharya, Bhattacharya, Ayan, Parthanil Roy +1
Economics, Econometrics and Finance · Mathematics · #37A40 (Secondary) #60G10 #60G60 #62H15 (Primary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:37A40 #msc:60G10 #msc:60G60 #msc:62H15 #stat.TH

paper · pdf · doi:10.48550/arxiv.1611.08874

Accepted for publication in Journal of Applied Probability

openalex publication_date 2016/11/27 · arxiv created 2017/11/27 · arxiv updated 2017/11/29 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

Based on the ratio of two block maxima, we propose a large sample test for the length of memory of a stationary symmetric α-stable discrete parameter random field. We show that the power function converges to one as the sample-size increases to infinity under various classes of alternatives having longer memory in the sense of Samorodnitsky(2004). Ergodic theory of nonsingular ℤ^d-actions play a very important role in the design and analysis of our large sample test.

Citations

• Log-Periodogram Regression of Time Series with Long Range Dependence
• Maximal Moments and Uniform Modulus of Continuity for Stable Random Fields

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