{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T19:57:38Z","timestamp":1776974258401,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T00:00:00Z","timestamp":1659052800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces methodologies in forecasting oil prices (Brent and WTI) with multivariate time series of major S&amp;P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. We also apply Bayesian variable selection and nonlinear principal component analysis (NLPCA) for data dimension reduction. With a reduced number of important covariates, we also forecast oil prices (Brent and WTI) with multivariate time series of major S&amp;P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. To apply real data to the proposed methods, we select monthly log returns of 2 oil prices and 74 large-cap, major S&amp;P 500 stock prices across the period of February 2001\u2013October 2019. We conclude that vine copula regression with NLPCA is superior overall to other proposed methods in terms of the measures of prediction errors.<\/jats:p>","DOI":"10.3390\/axioms11080375","type":"journal-article","created":{"date-parts":[[2022,7,31]],"date-time":"2022-07-31T21:49:02Z","timestamp":1659304142000},"page":"375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Forecasting Crude Oil Prices with Major S&amp;P 500 Stock Prices: Deep Learning, Gaussian Process, and Vine Copula"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3821-2060","authenticated-orcid":false,"given":"Jong-Min","family":"Kim","sequence":"first","affiliation":[{"name":"Statistics Discipline, University of Minnesota at Morris, Morris, MN 56267, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4304-8189","authenticated-orcid":false,"given":"Hope H.","family":"Han","sequence":"additional","affiliation":[{"name":"School of Business Administration, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2824-0850","authenticated-orcid":false,"given":"Sangjin","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Management and Information Systems, Dong-A University, Busan 49236, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.eneco.2015.11.015","article-title":"Quantile dependence of oil price movements and stock returns","volume":"54","author":"Reboredo","year":"2016","journal-title":"Energy Econ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.eneco.2014.11.018","article-title":"Has oil price predicted stock returns for over a century?","volume":"48","author":"Narayan","year":"2015","journal-title":"Energy Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1111\/ecin.12053","article-title":"Forecasting crude oil price movements with oil-sensitive stocks","volume":"52","author":"Chen","year":"2014","journal-title":"Econ. 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