{"paper":{"title":"Eigenvalue distribution of large sample covariance matrices of linear processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Eckhard Schlemm, Oliver Pfaffel","submitted_at":"2012-01-18T15:37:12Z","abstract_excerpt":"We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable $i=1,...,p$ is modelled as a linear process $(X_{i,t})_{t=1,...,n}=(\\sum_{j=0}^\\infty c_j Z_{i,t-j})_{t=1,...,n}$, where $\\{Z_{i,t}\\}$ are assumed to be independent random variables with finite fourth moments. If the sample size $n$ and the number of variables $p=p_n$ both converge to infinity such that $y=\\lim_{n\\to\\infty}{n/p_n}>0$, then the empirical spectral distribution of $p^{-1}\\X\\X^T$ converges to a non\\hyp{}random distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3828","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"}