{"paper":{"title":"Multiscale inference and long-run variance estimation in nonparametric regression with time series errors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marina Khismatullina, Michael Vogt","submitted_at":"2019-03-04T14:13:16Z","abstract_excerpt":"In this paper, we develop new multiscale methods to test qualitative hypotheses about the regression function m in a nonparametric regression model with fixed design points and time series errors. In time series applications, m represents a nonparametric time trend. Practitioners are often interested in whether the trend m has certain shape properties. For example, they would like to know whether m is constant or whether it is increasing/decreasing in certain time regions. Our multiscale methods allow to test for such shape properties of the trend m. In order to perform the methods, we require"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01253","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"}