{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T14:54:44Z","timestamp":1774536884535,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T00:00:00Z","timestamp":1681344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Basic and the Applied Basic Research Foundation","award":["2022A1515010046"],"award-info":[{"award-number":["2022A1515010046"]}]},{"name":"Guangdong Basic and the Applied Basic Research Foundation","award":["SL2022A03J00654"],"award-info":[{"award-number":["SL2022A03J00654"]}]},{"name":"Guangdong Basic and the Applied Basic Research Foundation","award":["2021GDJC-D02"],"award-info":[{"award-number":["2021GDJC-D02"]}]},{"name":"Science and Technology Projects in Guangzhou","award":["2022A1515010046"],"award-info":[{"award-number":["2022A1515010046"]}]},{"name":"Science and Technology Projects in Guangzhou","award":["SL2022A03J00654"],"award-info":[{"award-number":["SL2022A03J00654"]}]},{"name":"Science and Technology Projects in Guangzhou","award":["2021GDJC-D02"],"award-info":[{"award-number":["2021GDJC-D02"]}]},{"name":"The Graduate Innovation Research Funding Program of Guangzhou University","award":["2022A1515010046"],"award-info":[{"award-number":["2022A1515010046"]}]},{"name":"The Graduate Innovation Research Funding Program of Guangzhou University","award":["SL2022A03J00654"],"award-info":[{"award-number":["SL2022A03J00654"]}]},{"name":"The Graduate Innovation Research Funding Program of Guangzhou University","award":["2021GDJC-D02"],"award-info":[{"award-number":["2021GDJC-D02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The GARCH model is one of the most influential models for characterizing and predicting fluctuations in economic and financial studies. However, most traditional GARCH models commonly use daily frequency data to predict the return, correlation, and risk indicator of financial assets, without taking data with other frequencies into account. Hence, financial market information may not be sufficiently applied to the estimation of GARCH-type models. To partially solve this problem, this paper introduces intraday high-frequency data to improve estimation of the volatility function of a semiparametric GARCH model. To achieve this objective, a semiparametric volatility proxy model was proposed, which includes both symmetric and asymmetric cases. Under mild conditions, the asymptotic normality of estimators was established. Furthermore, we also discuss the impact of different volatility proxies on estimation precision. Both the simulation and empirical results showed that estimation of the volatility function could be improved by the introduction of high-frequency data.<\/jats:p>","DOI":"10.3390\/sym15040908","type":"journal-article","created":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T02:28:12Z","timestamp":1681439292000},"page":"908","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Daily Semiparametric GARCH Model Estimation Using Intraday High-Frequency Data"],"prefix":"10.3390","volume":"15","author":[{"given":"Fangrou","family":"Chai","sequence":"first","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Li","sequence":"additional","affiliation":[{"name":"Research Centre for Applied Mathematics, Shenzhen Polytechnic, ShenZhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingfa","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongxiu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"987","DOI":"10.2307\/1912773","article-title":"Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. Inflation","volume":"50","author":"Engle","year":"1982","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/0304-4076(86)90063-1","article-title":"Generalized autoregressive conditional heteroskedasticity","volume":"31","author":"Bollerslev","year":"1986","journal-title":"J. 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