{"paper":{"title":"Consistency of detrended fluctuation analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an","stat.TH"],"primary_cat":"math.ST","authors_text":"Ola L{\\o}vsletten","submitted_at":"2016-09-29T13:36:34Z","abstract_excerpt":"The scaling function $F(s)$ in detrended fluctuation analysis (DFA) scales as $F(s)\\sim s^{H}$ for stochastic processes with Hurst exponents $H$. We prove this scaling law for both stationary stochastic processes with $0<H<1$, and non-stationary stochastic processes with $1<H<2$. For $H<0.5$ we observe that using the asymptotic (power-law) auto-correlation function (ACF) yield $F(s)\\sim s^{1/2}$. We also show that the fluctuation function in DFA is equal in expectation to: i) A weighted sum of the ACF ii) A weighted sum of the second order structure function. These results enable us to compute"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09331","kind":"arxiv","version":2},"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"}