{"paper":{"title":"Prediction of weakly locally stationary processes by auto-regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andres Sanchez-Perez (LTCI), Fran\\c{c}ois Roueff (LTCI)","submitted_at":"2016-02-05T07:47:11Z","abstract_excerpt":"In this contribution we introduce weakly locally stationary time series  through the local approximation of the non-stationary covariance structure by  a stationary one.  This allows us to define autoregression coefficients in a  non-stationary context, which, in the particular case of a locally stationary  Time Varying Autoregressive (TVAR) process, coincide with the generating  coefficients. We provide and study an estimator of the time varying  autoregression coefficients in a general setting. The proposed estimator of  these coefficients enjoys an optimal minimax convergence rate under lim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01942","kind":"arxiv","version":3},"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"}