{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:57Z","timestamp":1760143677254,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T00:00:00Z","timestamp":1708560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2022A1515010046","SL2022A03J00654","202201010276","2022A1515110009"],"award-info":[{"award-number":["2022A1515010046","SL2022A03J00654","202201010276","2022A1515110009"]}]},{"name":"Science and Technology Projects in Guangzhou","award":["2022A1515010046","SL2022A03J00654","202201010276","2022A1515110009"],"award-info":[{"award-number":["2022A1515010046","SL2022A03J00654","202201010276","2022A1515110009"]}]},{"name":"Youth Joint Project of Department of Science and Technology in Guangdong Province of China","award":["2022A1515010046","SL2022A03J00654","202201010276","2022A1515110009"],"award-info":[{"award-number":["2022A1515010046","SL2022A03J00654","202201010276","2022A1515110009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The portmanteau test is an effective tool for testing the goodness of fit of models. Motivated by the fact that high-frequency data can improve the estimation accuracy of models, a modified portmanteau test using high-frequency data is proposed for ARCH-type models in this paper. Simulation results show that the empirical size and power of the modified test statistics of the model using high-frequency data are better than those of the daily model. Three stock indices (CSI 300, SSE 50, CSI 500) are taken as an example to illustrate the practical application of the test.<\/jats:p>","DOI":"10.3390\/axioms13030141","type":"journal-article","created":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T08:34:35Z","timestamp":1708590875000},"page":"141","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Portmanteau Test for ARCH-Type Models by Using High-Frequency Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5780-6812","authenticated-orcid":false,"given":"Yanshan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}]},{"given":"Xingfa","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}]},{"given":"Chunliang","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mathematics, Jiaying University, Meizhou 514015, China"}]},{"given":"Yujiao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,22]]},"reference":[{"key":"ref_1","first-page":"34","article-title":"The Variation of Certain Speculative Prices","volume":"39","author":"Samuelson","year":"1966","journal-title":"J. Bus."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hamilton, J.D. (1994). Time Series Analysis, Princeton University Press. [1st ed.].","DOI":"10.1515\/9780691218632"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"987","DOI":"10.2307\/1912773","article-title":"Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation","volume":"50","author":"Engle","year":"1982","journal-title":"Econometrica"},{"key":"ref_4","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. Econom."},{"key":"ref_5","unstructured":"Black, F. (1986). Proceedings of the 1976 Meeting of the Business and Economic Statistics Section, American Statistical Association."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1080\/07474938608800097","article-title":"Modeling The persistence of Conditional Variances: A Comment","volume":"5","author":"Geweke","year":"1986","journal-title":"Econom. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0927-5398(93)90006-D","article-title":"A long memory property of stock returns","volume":"1","author":"Engle","year":"1993","journal-title":"J. Empri. Financ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0304-4076(97)00042-0","article-title":"Efficient estimation in semiparametric GARCH models","volume":"81","author":"Drost","year":"1997","journal-title":"J. Econom."},{"key":"ref_9","first-page":"162","article-title":"GARCH parameter estimation using high-frequency data","volume":"9","author":"Visser","year":"2011","journal-title":"J. Financ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/s10255-015-0488-y","article-title":"Robust M-estimate of gjr model with high frequency data","volume":"31","author":"Huang","year":"2015","journal-title":"Acta Math. Appl. Sin."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1111\/j.1540-6261.1993.tb05128.x","article-title":"On the relation between the expected value and the volatility of the nominal excess return on stocks","volume":"48","author":"Glosten","year":"1993","journal-title":"J. Financ."},{"key":"ref_12","first-page":"436","article-title":"Robust Statistics: A Review","volume":"9","author":"Huber","year":"1981","journal-title":"Ann. Stat."},{"key":"ref_13","first-page":"115","article-title":"Composite quantile regression for garch models using high-frequency data","volume":"7","author":"Wang","year":"2018","journal-title":"Econ. Stat."},{"key":"ref_14","first-page":"2052","article-title":"The estimating method of var based on pgarch model with high-frequency data","volume":"37","author":"Fan","year":"2017","journal-title":"Syst. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7390","DOI":"10.1080\/03610918.2020.1836215","article-title":"On the test of the volatility proxy model","volume":"51","author":"Deng","year":"2022","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3455","DOI":"10.3934\/math.2021206","article-title":"Daily nonparametric ARCH(1) model estimation using intraday high frequency data","volume":"6","author":"Liang","year":"2021","journal-title":"AIMS Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1080\/01621459.1970.10481180","article-title":"Distribution of Residual Autocorrelations in Autoregressive Integrated Moving Average Time Series Models","volume":"65","author":"Box","year":"1970","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","first-page":"7","article-title":"An introduction to bilinear time series models","volume":"8","author":"Granger","year":"1978","journal-title":"Int. Stat. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1111\/j.1467-9892.1983.tb00373.x","article-title":"Diagnostic Checking ARMA Time Series Models Using Squared-Residual Autocorrelations","volume":"4","author":"McLeod","year":"1983","journal-title":"J. Time Ser. Anal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/07474938608800095","article-title":"Modelling the persistence of conditional variances","volume":"5","author":"Engle","year":"1986","journal-title":"Econom. Rev."},{"key":"ref_21","first-page":"119","article-title":"Estimation of Autoregressive Models with Arch Errors","volume":"50","author":"Pantula","year":"1988","journal-title":"Sankhy\u0101 Indian J. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1111\/j.1467-9892.1994.tb00217.x","article-title":"On the squared residual autocorrelations in non-linear time series with conditional heteroskedasticity","volume":"15","author":"Li","year":"1994","journal-title":"J. Time Ser. Anal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1093\/biomet\/90.4.967","article-title":"Least absolute deviations estimation for ARCH and GARCH models","volume":"90","author":"Peng","year":"2003","journal-title":"Biometrika"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1093\/biomet\/92.3.691","article-title":"Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach","volume":"92","author":"Li","year":"2005","journal-title":"Biometrika"},{"key":"ref_25","first-page":"55","article-title":"Portmanteau Goodness-of-Fit Test for Asymmetric Power GARCH Models","volume":"40","author":"Carbon","year":"2011","journal-title":"Aust. N. Z. J. Stat."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.jeconom.2015.03.025","article-title":"Sign-based portmanteau test for ARCH-type models with heavy-tailed innovations","volume":"189","author":"Chen","year":"2015","journal-title":"J. Econom."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107321","DOI":"10.1016\/j.csda.2021.107321","article-title":"Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors","volume":"165","author":"Li","year":"2022","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_28","first-page":"1120","article-title":"Monte Carlo Calculations in Problems of Mathematical Physics","volume":"53","author":"Ulam","year":"1947","journal-title":"Bull. New Ser. Am. Math. Soc."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1103\/PhysRev.36.823","article-title":"Carlo Calculations in Problems of Mathematical Physics","volume":"36","author":"Uhlenbeck","year":"1930","journal-title":"Phys. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/14786442808674769","article-title":"A Brief Account of Microscopical Observations Made in the Months of June, July and August, 1827, on the Particles Contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies","volume":"4","author":"Brown","year":"1828","journal-title":"Philos. Mag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.jeconom.2007.06.004","article-title":"Estimation and tests for power-transformed and threshold GARCH models","volume":"142","author":"Pan","year":"2008","journal-title":"J. Econom."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/141\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:02:58Z","timestamp":1760104978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/141"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,22]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["axioms13030141"],"URL":"https:\/\/doi.org\/10.3390\/axioms13030141","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,2,22]]}}}