{"paper":{"title":"Iterated scaling limits for aggregation of random coefficient AR(1) and INAR(1) processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fanni Ned\\'enyi, Gyula Pap","submitted_at":"2016-01-18T20:14:06Z","abstract_excerpt":"We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of strictly stationary AR(1) and INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\\alpha \\in (0, 1)$ and idiosyncratic innovations. Assuming that $\\alpha$ has a density function of the form $\\psi(x) (1 - x)^\\beta$, $x \\in (0, 1)$, with $\\lim_{x\\uparrow 1} \\psi(x) = \\psi_1 \\in (0, \\infty)$, different Brownian limit processes of appropriately centered and scaled aggregated partial sums are shown to exist in case $\\beta=1$ when taking first the limit as $N \\to \\infty$ and then "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04679","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"}