{"paper":{"title":"The significance of trends in long-term correlated records","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ao-ph"],"primary_cat":"physics.data-an","authors_text":"Araik Tamazian, Armin Bunde, Josef Ludescher","submitted_at":"2014-11-14T13:26:59Z","abstract_excerpt":"We study the distribution $P(x;\\alpha,L)$ of the relative trend $x$ in long-term correlated records of length $L$ that are characterized by a Hurst-exponent $\\alpha$ between 0.5 and 1.5 obtained by DFA2. The relative trend $x$ is the ratio between the strength of the trend $\\Delta$ in the record measured by linear regression, and the standard deviation $\\sigma$ around the regression line. We consider $L$ between 400 and 2200, which is the typical length scale of monthly local and annual reconstructed global climate records. Extending previous work by Lennartz and Bunde \\cite{Lennartz2011} we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3903","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}