{"paper":{"title":"Persistence versus stability for auto-regressive processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir Dembo, Jian Ding, Jun Yan","submitted_at":"2019-06-02T19:51:46Z","abstract_excerpt":"The stability of an Auto-Regressive (AR) time sequence of finite order $L$, is determined by the maximal modulus $r^\\star$ among all zeros of its generating polynomial. If $r^\\star<1$ then the effect of input and initial conditions decays rapidly in time, whereas for $r^\\star>1$ it is exponentially magnified (with constant or polynomially growing oscillations when $r^\\star=1$). Persistence of such AR sequence (namely staying non-negative throughout $[0,N]$) with decent probability, requires the largest positive zero of the generating polynomial to have the largest multiplicity among all zeros "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00473","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"}