{"paper":{"title":"Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Donatas Surgailis, Vytaute Pilipauskaite","submitted_at":"2013-10-19T18:11:50Z","abstract_excerpt":"We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of AR(1) process with random-coefficient $a \\in [0,1)$ when $N$ and time scale $n$ increase at different rate. Assuming that $a$ has a density, regularly varying at $a = 1$ with exponent $-1 < \\beta < 1$, different joint limits of normalized aggregated partial sums are shown to exist when $N^{1/(1+\\beta)}/n$ tends to (i) $\\infty$, (ii) 0, (iii) $0 < \\mu < \\infty$. The limit process arising under (iii) admits a Poisson integral representation on $(0,\\infty) \\times C(\\mathbb{R})$ and enjoys \"intermediate\" propert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5257","kind":"arxiv","version":2},"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"}