{"id":2407,"date":"2024-11-18T19:00:21","date_gmt":"2024-11-18T11:00:21","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2407"},"modified":"2024-12-28T23:04:29","modified_gmt":"2024-12-28T15:04:29","slug":"%e5%b8%b8%e6%99%8b%e6%ba%90-delaigle-a-hall-p-tang-c-y-2018-a-frequency-domain-analysis-of-the-error-distribution-from-noisy-high-frequency-data-biometrika-105-353-369","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/publications\/publications-all\/2407\/","title":{"rendered":"\u5e38\u664b\u6e90, Delaigle, A., Hall, P., &#038; Tang, C. Y. (2018). A frequency domain analysis of the error distribution from noisy high-frequency data. Biometrika, 105, 353-369."},"content":{"rendered":"<p>Data observed at a high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or smooth random function, and measurement error. Supposing that the latent component is an Ito\u0302 diffusion process, we propose to estimate the measurement error density function by applying a deconvolu- tion technique with appropriate localization. Our estimator, which does not require equally-spaced observed times, is consistent and minimax rate-optimal. We also investigate estimators of the moments of the error distribution and their properties, propose a frequency domain estimator for the integrated volatility of the underlying stochastic process, and show that it achieves the optimal convergence rate. Simulations and an application to real data validate our analysis.<\/p>\r\n\r\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" style=\"width: 100%; height: 600px;\" data=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/A-frequency-domain-analysis-of-the-error-distribution-from-noisy-high-frequency-data.pdf\" type=\"application\/pdf\" width=\"300\" height=\"150\" aria-label=\"\u5d4c\u5165 &lt;strong&gt;&lt;mark style=&quot;background-color:rgba(0, 0, 0, 0)&quot; class=&quot;has-inline-color has-vivid-cyan-blue-color&quot;&gt;A frequency domain analysis of the error distribution from noisy high-frequency data.pdf&lt;\/mark&gt;&lt;\/strong&gt;\"><\/object><a id=\"wp-block-file--media-c1ebffaa-c5ea-4605-8550-6d86ce9c0f65\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/A-frequency-domain-analysis-of-the-error-distribution-from-noisy-high-frequency-data.pdf\"><strong><mark class=\"has-inline-color has-vivid-cyan-blue-color\" style=\"background-color: rgba(0, 0, 0, 0);\">A frequency domain analysis of the error distribution from noisy high-frequency data.pdf<\/mark><\/strong><\/a><a class=\"wp-block-file__button wp-element-button\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/A-frequency-domain-analysis-of-the-error-distribution-from-noisy-high-frequency-data.pdf\" download=\"\" aria-describedby=\"wp-block-file--media-c1ebffaa-c5ea-4605-8550-6d86ce9c0f65\">\u4e0b\u8f7d<\/a><\/div>\r\n","protected":false},"excerpt":{"rendered":"<p>Data observed at a high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or smooth random function, and measurement error. Supposing that the latent component is an Ito\u0302 diffusion process, we propose to estimate the measurement error density function by applying a deconvolu- tion technique with appropriate localization. Our estimator, which does not require equally-spaced observed times, is consistent and minimax rate-optimal. We also investigate estimators of the moments of the error distribution and their properties, propose a frequency domain estimator for the integrated volatility of the underlying stochastic process, and show that it achieves the optimal convergence rate. Simulations and an application to real data validate our analysis.<\/p>\n","protected":false},"author":1,"featured_media":2408,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[15],"tags":[],"class_list":["post-2407","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publications-all"],"acf":[],"lang":"cn","translations":{"cn":2407,"en":2411},"pll_sync_post":[],"_links":{"self":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2407","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/comments?post=2407"}],"version-history":[{"count":5,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2407\/revisions"}],"predecessor-version":[{"id":3916,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2407\/revisions\/3916"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media\/2408"}],"wp:attachment":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media?parent=2407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/categories?post=2407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/tags?post=2407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}