{"paper":{"title":"Hidden regular variation of moving average processes with heavy-tailed innovations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joyjit Roy, Sideny I. Resnick","submitted_at":"2013-09-30T16:28:59Z","abstract_excerpt":"We look at joint regular variation properties of MA($\\infty$) processes of the form $\\mathbf{X} = (X_k, k \\in \\mathbb{Z})$ where $X_k = \\sum_{j=0}^{\\infty} \\psi_j Z_{k-j}$ and the sequence of random variables $(Z_i, i \\in \\mathbb{Z})$ are i.i.d. with regularly varying tails. We use the setup of $\\mathbb{M}_{\\mathbb{O}}$-convergence and obtain hidden regular variation properties for $\\mathbf{X}$ under suitable summability conditions on the constant coefficients $(\\psi_j : j \\geq 0)$. Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7909","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"}