{"paper":{"title":"High-frequency sampling and kernel estimation for continuous-time moving average processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Claudia Kl\\\"uppelberg, Peter Brockwell, Vincenzo Ferrazzano","submitted_at":"2011-07-22T09:57:45Z","abstract_excerpt":"Interest in continuous-time processes has increased rapidly in recent years, largely because of high-frequency data available in many applications. We develop a method for estimating the kernel function $g$ of a second-order stationary L\\'evy-driven continuous-time moving average (CMA) process $Y$ based on observations of the discrete-time process $Y^\\Delta$ obtained by sampling $Y$ at $\\Delta, 2\\Delta,...,n\\Delta$ for small $\\Delta$. We approximate $g$ by $g^\\Delta$ based on the Wold representation and prove its pointwise convergence to $g$ as $\\Delta\\rightarrow 0$ for $\\CARMA(p,q)$ processes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4468","kind":"arxiv","version":4},"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"}