{"paper":{"title":"Estimation of volatility functionals: the case of a square root n window","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean Jacod (IMJ), Mathieu Rosenbaum (LPMA)","submitted_at":"2012-12-10T09:01:26Z","abstract_excerpt":"We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/\\Delta_n, with \\Delta_n going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the volatility matrix, with the optimal rate 1/\\sqrt{\\Delta_n} and minimal asymptotic variance. To achieve this we use spot volatility estimators based on observations within time intervals of length k_n\\Delta_n. In [5] this was done with k_n tending to infinity and k_n\\sqrt{\\Delta_n} tending to 0, and a central limit theorem was given after suitable de-biasing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1997","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"}