{"paper":{"title":"Testing epidemic change in nearly nonstationary process with statistics based on residuals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alfredas Ra\\v{c}kauskas, Charles Suquet, Jurgita Markevi\\v{c}i\\=ut\\.e","submitted_at":"2014-10-18T10:33:14Z","abstract_excerpt":"We study an epidemic type change in innovations of a first order autoregressive process $ y_{n,k} = \\varphi_n y_{n,k-1} + \\epsilon_{k} + a_{n,k}$, where $\\phi_n$ is either a constant in $(-1,1)$ or a sequence in $(0,1)$, converging to 1. For $k$ inside some unknown interval $\\mathbb{I}_n^\\ast=(k^\\ast,k^\\ast+\\ell^\\ast]$, $a_{n,k}=a_n$ while $a_{n,k}=0$ for $k$ outside $\\mathbb{I}_n^\\ast$. When $a_n\\neq 0$, we have an epidemic deviation from the usual (zero) mean of innovations. Since innovations are not observed, we build uniform increments statistics on residuals $(\\widehat{\\epsilon}_k)$ of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4945","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"}