{"paper":{"title":"Invariance Principles for Tempered Fractionally Integrated Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Donatas Surgailis, Farzad Sabzikar","submitted_at":"2017-03-07T16:49:08Z","abstract_excerpt":"We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in $\\alpha$-stable $(1< \\alpha \\le 2)$ i.i.d. innovations and related tempered linear processes with vanishing tempering parameter $\\lambda \\sim \\lambda_*/N$. We show that the limit of the partial sums process takes a different form in the weakly tempered ($\\lambda_* = 0$), strongly tempered ($\\lambda_* = \\infty$), and moderately tempered ($0<\\lambda_* < \\infty$) cases. These results are used to derive the limit distribution of the OLS estimate of AR(1) unit root with weakly, strongly, and mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02467","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"}