{"paper":{"title":"Asymptotic probability distribution of distances between local extrema of error terms of a moving average process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Argyn Kuketayev","submitted_at":"2011-05-23T03:19:45Z","abstract_excerpt":"Consider error terms x(i) of a moving average process MA(q), where x(i)=e(i) + e(i-1)+...+e(i-q) and e(i) - independent identically distributed (i.i.d.) random variables. We recognize a term x(i) as a local maximum if the following condition holds true: x(i-1) < x(i) > x(i+1). If the local maximum x(i) is followed by the next local maxiumum x(k), then d=k-i is the distance between local maxima. The distances d(j) themselves are random vriables. In this paper we study the probability distribution of distances d(j). Particularly, we show that for any q>0 mean distance E[d(j)]=4 and asymptoticall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4396","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"}