{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T07:14:33Z","timestamp":1775459673026,"version":"3.50.1"},"reference-count":86,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J of Applied Econometrics"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>We revisit maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE work in this context. First, the hemispheres share a common core at the entrance of the network, which accommodates various forms of time variation in the error variance. Second, we introduce a volatility emphasis constraint that breaks mean\/variance indeterminacy in this class of overparametrized nonlinear models. Third, we conduct a blocked out\u2010of\u2010bag reality check to curb overfitting in both conditional moments. Fourth, the algorithm utilizes standard deep learning software and thus handles large data sets\u2010both computationally and statistically. Ergo, our hemisphere neural network (HNN) provides proactive volatility forecasts based on leading indicators when it can, and reactive volatility based on the magnitude of previous prediction errors when it must. We evaluate point and density forecasts with an extensive out\u2010of\u2010sample experiment and benchmark against a suite of models ranging from classics to more modern machine learning\u2010based offerings. In all cases, HNN fares well by consistently providing accurate mean\/variance forecasts for all targets and horizons. Studying the resulting volatility paths reveals its versatility, while probabilistic forecasting evaluation metrics showcase its enviable reliability. Finally, we also demonstrate how this machinery can be merged with other structured deep learning models by revisiting Goulet Coulombe (2025)'s neural Phillips curve.<\/jats:p>","DOI":"10.1002\/jae.70042","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T15:25:58Z","timestamp":1768404358000},"page":"265-279","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["From Reactive to Proactive Volatility Modeling With Hemisphere Neural Networks"],"prefix":"10.1002","volume":"41","author":[{"given":"Philippe","family":"Goulet Coulombe","sequence":"first","affiliation":[{"name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al  Montreal Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikael","family":"Frenette","sequence":"additional","affiliation":[{"name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al  Montreal Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karin","family":"Klieber","sequence":"additional","affiliation":[{"name":"Oesterreichische Nationalbank  Vienna Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2021.01.003"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1257\/aer.20161923"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2943"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/18-AOS1709"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2022.10.005"},{"key":"e_1_2_9_7_1","doi-asserted-by":"crossref","unstructured":"Barunik J. andL.Hanus.2022.\u201cLearning Probability Distributions in Macroeconomics and Finance \u201darXiv Preprint arXiv:2204.06848.","DOI":"10.2139\/ssrn.4083719"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1903070116"},{"key":"e_1_2_9_9_1","volume-title":"Aston University Neural Computing Research Group Report","author":"Bishop C. M.","year":"1994"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90063-1"},{"key":"e_1_2_9_11_1","volume-title":"The Anatomy of Out\u2010Of\u2010Sample Forecasting Accuracy. Working Paper No. 2022\u201016","author":"Borup D.","year":"2022"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.0025"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00477-018-1573-6"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1162\/rest_a_00693"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2442"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1920\/wp.cem.2018.1618"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOAS285"},{"key":"e_1_2_9_18_1","volume-title":"Forecasting Value\u2010At\u2010Risk Using Deep Neural Network Quantile Regression. Finance Centre Working Papers","author":"Chronopoulos I.","year":"2023"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/iere.12619"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.2509"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2023.2277171"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1057\/s41260-021-00237-x"},{"key":"e_1_2_9_23_1","volume-title":"Confidence Intervals and Prediction Intervals for Feed\u2010Forward Neural Networks","author":"Dybowski R.","year":"2001"},{"key":"e_1_2_9_24_1","unstructured":"ECB.2012.\u201cVerbatim of the Remarks Made by Mario Draghi. Speech by Mario Draghi \u201d President of the European Central Bank at the Global Investment Conference in London July 26."},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912773"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00300"},{"key":"e_1_2_9_27_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913242"},{"key":"e_1_2_9_28_1","unstructured":"Farrell M. H. T.Liang andS.Misra.2020.\u201cDeep Learning for Individual Heterogeneity \u201darXiv preprint arXiv:2010.14694."},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347963"},{"key":"e_1_2_9_30_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913241"},{"key":"e_1_2_9_31_1","doi-asserted-by":"publisher","DOI":"10.1198\/073500105000000018"},{"key":"e_1_2_9_32_1","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00317"},{"key":"e_1_2_9_33_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000001437"},{"key":"e_1_2_9_34_1","unstructured":"Goulet Coulombe P.2020.\u201cTime\u2010Varying Parameters As Ridge Regressions \u201darXiv preprint arXiv:2009.00401."},{"key":"e_1_2_9_35_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.3030"},{"key":"e_1_2_9_36_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2024.2421279"},{"key":"e_1_2_9_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2021.05.005"},{"key":"e_1_2_9_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1860-9"},{"key":"e_1_2_9_39_1","unstructured":"Graves A.2013.\u201cGenerating Sequences With Recurrent Neural Networks \u201darXiv preprint arXiv:1308.0850."},{"key":"e_1_2_9_40_1","doi-asserted-by":"publisher","DOI":"10.1214\/10-BA507"},{"key":"e_1_2_9_41_1","doi-asserted-by":"crossref","unstructured":"Grinsztajn L. E.Oyallon andG.Varoquaux.2022.\u201cWhy do Tree\u2010Based Models Still Outperform Deep Learning on Tabular Data? \u201darXiv preprint arXiv:2207.08815.","DOI":"10.52202\/068431-0037"},{"key":"e_1_2_9_42_1","doi-asserted-by":"crossref","unstructured":"Guidolin M. D.La Cara andM. G.Marcellino.2021.\u201cBoosting the Forecasting Power of Conditional Heteroskedasticity Models to Account for Covid\u201019 Outbreaks \u201d BAFFI CAREFIN Centre Research Paper (2021\u2010169).","DOI":"10.2139\/ssrn.3992584"},{"key":"e_1_2_9_43_1","first-page":"1321","volume-title":"International Conference on Machine Learning","author":"Guo C.","year":"2017"},{"key":"e_1_2_9_44_1","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOS2133"},{"key":"e_1_2_9_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2022.03.002"},{"key":"e_1_2_9_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2024.105843"},{"key":"e_1_2_9_47_1","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"e_1_2_9_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90020-8"},{"key":"e_1_2_9_49_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2020.11.006"},{"key":"e_1_2_9_50_1","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOAS1488"},{"key":"e_1_2_9_51_1","doi-asserted-by":"publisher","DOI":"10.1198\/073500102753410408"},{"key":"e_1_2_9_52_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2013.01.002"},{"key":"e_1_2_9_53_1","doi-asserted-by":"publisher","DOI":"10.1111\/jofi.13298"},{"key":"e_1_2_9_54_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijepes.2014.03.060"},{"key":"e_1_2_9_55_1","doi-asserted-by":"crossref","unstructured":"Kn\u00fcppel M. F.Kr\u00fcger andM.\u2010O.Pohle.2022.Score\u2010Based Calibration Testing for Multivariate Forecast DistributionsarXiv preprint arXiv:2211.16362.","DOI":"10.2139\/ssrn.4350792"},{"key":"e_1_2_9_56_1","volume-title":"Bayesian Econometrics","author":"Koop G. M.","year":"2003"},{"key":"e_1_2_9_57_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2010.496117"},{"key":"e_1_2_9_58_1","article-title":"Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles","volume":"30","author":"Lakshminarayanan B.","year":"2017","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_9_59_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2012.751873"},{"key":"e_1_2_9_60_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.euroecorev.2025.105079"},{"key":"e_1_2_9_61_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2019.07.113"},{"key":"e_1_2_9_62_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v32i1.12124"},{"key":"e_1_2_9_63_1","volume-title":"Fred\u2010qd: A Quarterly Database for Macroeconomic Research Technical Report","author":"McCracken M.","year":"2020"},{"key":"e_1_2_9_64_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2015.1086655"},{"key":"e_1_2_9_65_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2019.1637745"},{"key":"e_1_2_9_66_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2021.1909601"},{"key":"e_1_2_9_67_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.1992.10509902"},{"key":"e_1_2_9_68_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.11570"},{"key":"e_1_2_9_69_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1994.tb01956.x"},{"key":"e_1_2_9_70_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICNN.1994.374138"},{"key":"e_1_2_9_71_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfineco.2012.06.005"},{"key":"e_1_2_9_72_1","first-page":"2627","volume-title":"Proceedings of the 26th International Joint Conference on Artificial Intelligence","author":"Qin Y.","year":"2017"},{"issue":"1","key":"e_1_2_9_73_1","first-page":"335","article-title":"Early Stopping and Non\u2010Parametric Regression: An Optimal Data\u2010Dependent Stopping Rule","volume":"15","author":"Raskutti G.","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_9_74_1","doi-asserted-by":"publisher","DOI":"10.1038\/323533a0"},{"key":"e_1_2_9_75_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijforecast.2019.07.001"},{"key":"e_1_2_9_76_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2018.1506342"},{"key":"e_1_2_9_77_1","doi-asserted-by":"crossref","unstructured":"Smalter Hall A. andT. R.Cook.2017.\u201cMacroeconomic Indicator Forecasting With Deep Neural Networks \u201d Federal Reserve Bank of Kansas City Working Paper (17\u201311).","DOI":"10.2139\/ssrn.3046657"},{"key":"e_1_2_9_78_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3932(99)00027-6"},{"key":"e_1_2_9_79_1","doi-asserted-by":"publisher","DOI":"10.1002\/1099-131X(200007)19:4<299::AID-FOR775>3.0.CO;2-V"},{"key":"e_1_2_9_80_1","first-page":"203","article-title":"Financial Returns Modelled by the Product of Two Stochastic Processes\u2010a Study of the Daily Sugar Prices 1961\u201075","volume":"1","author":"Taylor S. J.","year":"1982","journal-title":"Time Series Analysis: Theory and Practice"},{"key":"e_1_2_9_81_1","volume-title":"Algorithmic Learning in a Random World","author":"Vovk V.","year":"2005"},{"key":"e_1_2_9_82_1","unstructured":"Wen R. K.Torkkola B.Narayanaswamy andD.Madeka.2017.\u201cA Multi\u2010Horizon Quantile Recurrent Forecaster \u201darXiv preprint arXiv:1711.11053."},{"key":"e_1_2_9_83_1","volume-title":"Introductory Econometrics: A Modern Approach","author":"Wooldridge J. M.","year":"2016"},{"key":"e_1_2_9_84_1","doi-asserted-by":"publisher","DOI":"10.1002\/for.3003"},{"key":"e_1_2_9_85_1","unstructured":"Yin Z. andP.Barucca.2022a.\u201cNeural Generalised Autoregressive Conditional Heteroskedasticity \u201darXiv preprint arXiv:2202.11285."},{"key":"e_1_2_9_86_1","unstructured":"Yin Z. andP.Barucca.2022b.\u201cVariational Heteroscedastic Volatility Model \u201darXiv preprint arXiv:2204.05806."},{"key":"e_1_2_9_87_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2018.2840738"}],"container-title":["Journal of Applied Econometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jae.70042","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/jae.70042","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jae.70042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T06:26:51Z","timestamp":1775456811000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jae.70042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":86,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10.1002\/jae.70042"],"URL":"https:\/\/doi.org\/10.1002\/jae.70042","archive":["Portico"],"relation":{},"ISSN":["0883-7252","1099-1255"],"issn-type":[{"value":"0883-7252","type":"print"},{"value":"1099-1255","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,14]]},"assertion":[{"value":"2025-12-30","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}