{"paper":{"title":"On the variances of a spatial unit root model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"S\\'andor Baran","submitted_at":"2010-06-29T21:01:02Z","abstract_excerpt":"The asymptotic properties of the variances of the spatial autoregressive model $X_{k,\\ell}=\\alpha X_{k-1,\\ell}+\\beta X_{k,\\ell-1}+\\gamma X_{k-1,\\ell-1}+\\epsilon_{k,\\ell}$ are investigated in the unit root case, that is when the parameters are on the boundary of domain of stability that forms a tetrahedron in $[-1,1]^3$. The limit of the variance of $n^{-\\varrho}X_{[ns],[nt]}$ is determined, where on the interior of the faces of the domain of stability $\\varrho=1/4$, on the edges $\\varrho =1/2$, while on the vertices $\\varrho =1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5730","kind":"arxiv","version":3},"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"}