{"paper":{"title":"A generalized nonlinear model for long memory conditional heteroscedasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andrius \\v{S}karnulis, Ieva Grublyt\\.e","submitted_at":"2015-09-05T15:12:30Z","abstract_excerpt":"We study the existence and properties of stationary solution of ARCH-type equation $r_t= \\zeta_t \\sigma_t$, where $\\zeta_t$ are standardized i.i.d. r.v.'s and the conditional variance satisfies an AR(1) equation $\\sigma^2_t = Q^2\\big(a + \\sum_{j=1}^\\infty b_j r_{t-j}\\big) + \\gamma \\sigma^2_{t-1}$ with a Lipschitz function $Q(x)$ and real parameters $a, \\gamma, b_j $. The paper extends the model and the results in Doukhan et al. (2015) from the case $\\gamma = 0$ to the case $0< \\gamma < 1$. We also obtain a new condition for the existence of higher moments of $r_t$ which does not include the Ro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01708","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"}