{"paper":{"title":"Explicit Form of Coefficients in any MA(2) Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eugene Seneta, Simon Ku","submitted_at":"2014-05-27T21:20:43Z","abstract_excerpt":"We shall show that for {\\it any} $MA(2)$ process (apart from those with coefficients $\\theta_1,\\theta_2 $ lying on certain line-segments) there is {\\it one and only one invertible} $MA(2)$ process with the {\\it same} autocovariances $\\gamma_0,\\gamma_1,\\gamma_2$. It is this invertible version which computer-packages fit, regardless, even if data came from a non-invertible $MA(2)$ process. This has consequences for prediction from a fitted process, inasmuch as such prediction would seem to be inappropriate. We express the coefficients $\\theta_1,\\theta_2 $ of the invertible version in terms of $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7067","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"}