English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We apply the concept of distance covariance for testing independence of twolong-range dependent time series. As test statistic we propose a linearcombination of empirical distance cross-covariances. We derive the asymptoticdistribution of the test statistic, and we show consistency against arbitraryalternatives. The asymptotic theory developed in this paper is based on a novelnon-central limit theorem for stochastic processes with values in an$L^2$-Hilbert space. This limit theorem is of general theoretical interestwhich goes beyond the context of this article. Subject to the dependence in thedata, the standardization and the limit distributions of the proposed teststatistic vary. Since the limit distributions are unknown, we propose asubsampling procedure to determine the critical values for the proposed test,and we provide a proof for the validity of subsampling. In a simulation study,we investigate the finite-sample behavior of our test, and we compare itsperformance to tests based on the empirical cross-covariances. As anapplication of our results we analyze the cross-dependencies between meanmonthly discharges of three rivers.

Test for independence of long-range dependent time series using distance covariance