{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T05:05:23Z","timestamp":1791263123570,"version":"4.1.0"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2021,6,25]],"date-time":"2021-06-25T00:00:00Z","timestamp":1624579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,5,25]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimated factors to derive the reduced data for subsequent forecasting. Using directional regression and the inverse third-moment method in the stage of sufficient dimension reduction, the proposed methods can capture the nonmonotone effect of factors on the response. We also allow a diverging number of factors and only impose general regularity conditions on the distribution of factors, avoiding the undesired time reversibility of the factors by the latter. These make the proposed methods fundamentally more applicable than the sufficient forecasting method of Fan et al. (2017). The proposed methods are demonstrated both in simulation studies and an empirical study of forecasting monthly macroeconomic data from 1959 to 2016. Also, our theory contributes to the literature of sufficient dimension reduction, as it includes an invariance result, a path to perform sufficient dimension reduction under the high-dimensional setting without assuming sparsity, and the corresponding order-determination procedure.<\/jats:p>","DOI":"10.1093\/biomet\/asab037","type":"journal-article","created":{"date-parts":[[2021,6,23]],"date-time":"2021-06-23T19:11:28Z","timestamp":1624475488000},"page":"473-487","source":"Crossref","is-referenced-by-count":12,"title":["Inverse moment methods for sufficient forecasting using high-dimensional predictors"],"prefix":"10.1093","volume":"109","author":[{"given":"Wei","family":"Luo","sequence":"first","affiliation":[{"name":"Center for Data Science, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8252-0637","authenticated-orcid":false,"given":"Lingzhou","family":"Xue","sequence":"additional","affiliation":[{"name":"Department of Statistics, Pennsylvania State University, 318 Thomas Building, University Park, Pennsylvania 16802, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiawei","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Operations Research and Financial Engineering, Princeton University, Sherrerd Hall, Princeton, New Jersey 08544, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiufan","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, 102G Crowley Hall, Notre Dame, Indiana 46556, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,6,25]]},"reference":[{"key":"2022052609543456200_B1","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.3982\/ECTA8968","article-title":"Eigenvalue ratio test for the number of factors","volume":"81","author":"Ahn,","year":"2013","journal-title":"Econometrica"},{"key":"2022052609543456200_B2","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/1468-0262.00273","article-title":"Determining the number of factors in approximate factor models","volume":"70","author":"Bai,","year":"2002","journal-title":"Econometrica"},{"key":"2022052609543456200_B3","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.jeconom.2008.08.010","article-title":"Forecasting economic time series using targeted predictors","volume":"146","author":"Bai,","year":"2008","journal-title":"J. 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