{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T13:09:39Z","timestamp":1776690579378,"version":"3.51.2"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2016,10,27]],"date-time":"2016-10-27T00:00:00Z","timestamp":1477526400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p>Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. In order to address this issue, a novel criterion for forecast evaluation that utilizes the entire distribution of forecast errors is introduced. In particular, we introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority; and we develop tests for GL (CL) superiority that are based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi, and Whang (2005,<jats:italic>Review of Economic Studies<\/jats:italic>72, 735\u2013765). Our test statistics are characterized by nonstandard limiting distributions, under the null, necessitating the use of resampling procedures to obtain critical values. Additionally, the tests are consistent and have nontrivial local power, under a sequence of local alternatives. The above theory is developed for the stationary case, as well as for the case of heterogeneity that is induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples, and an application in which we examine exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.<\/jats:p>","DOI":"10.1017\/s0266466616000426","type":"journal-article","created":{"date-parts":[[2016,10,27]],"date-time":"2016-10-27T09:26:58Z","timestamp":1477560418000},"page":"1306-1351","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":19,"title":["ROBUST FORECAST COMPARISON"],"prefix":"10.1017","volume":"33","author":[{"given":"Sainan","family":"Jin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentina","family":"Corradi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Norman R.","family":"Swanson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,10,27]]},"reference":[{"key":"S0266466616000426_ref15","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1017\/S0266466600006629","article-title":"Stochastic equicontinuity for unbounded dependent heterogeneous arrays","volume":"12","author":"Hansen","year":"1996","journal-title":"Econometric Theory"},{"key":"S0266466616000426_ref6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1111\/j.1468-2354.2007.00418.x","article-title":"Nonparametric bootstrap procedures for predictive inference based on recursive estimation schemes","volume":"48","author":"Corradi","year":"2007","journal-title":"International Economic Review"},{"key":"S0266466616000426_ref3","unstructured":"Corradi, V. , Jin, S. , & Swanson, N.R. (2016) Improved Tests for Robust Forecast Comparison. Mimeo, University of Surrey."},{"key":"S0266466616000426_ref19","first-page":"65","article-title":"A simple sequentially rejective multiple test procedure","volume":"6","author":"Holm","year":"1979","journal-title":"Scandinavian Journal of Statistics"},{"key":"S0266466616000426_ref21","unstructured":"Klecan, L. , McFadden, R. , & McFadden, D. (1991) A Robust Test for Stochastic Dominance. Working paper, Department of Economics, MIT."},{"key":"S0266466616000426_ref5","first-page":"194","volume-title":"Handbook of Economic Forecasting","volume":"1","author":"Corradi","year":"2006"},{"key":"S0266466616000426_ref14","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1093\/biomet\/82.3.561","article-title":"On blocking rules for the bootstrap with dependent data","volume":"82","author":"Hall","year":"1995","journal-title":"Biometrika"},{"key":"S0266466616000426_ref29","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1111\/1468-0262.00152","article-title":"A reality check for data snooping","volume":"68","author":"White","year":"2000","journal-title":"Econometrica"},{"key":"S0266466616000426_ref27","article-title":"Empirical Processes: Theory and Applications","volume":"2","author":"Pollard","year":"1990","journal-title":"CBMS Conference Series in Probability and Statistic"},{"key":"S0266466616000426_ref20","doi-asserted-by":"crossref","first-page":"104","DOI":"10.2307\/3666023","article-title":"A stochastic dominance approach to evaluating foreign exchange hedging strategies","volume":"21","author":"Hunter","year":"1992","journal-title":"Financial Management"},{"key":"S0266466616000426_ref23","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.jeconom.2009.08.002","article-title":"An improved bootstrap test of stochastic dominance","volume":"154","author":"Linton","year":"2010","journal-title":"Journal of Econometrics"},{"key":"S0266466616000426_ref16","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1198\/073500105000000063","article-title":"A test for superior predictive ability","volume":"23","author":"Hansen","year":"2005","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466616000426_ref26","first-page":"461","article-title":"Limit theorems for weakly dependent Hilbert space valued random variables with application to the stationary bootstrap","volume":"4","author":"Politis","year":"1994","journal-title":"Statistica Sinica"},{"key":"S0266466616000426_ref28","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.2307\/2171956","article-title":"Asymptotic inference about predictive ability","volume":"64","author":"West","year":"1996","journal-title":"Econometrica"},{"key":"S0266466616000426_ref24","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0304-4076(00)00022-1","article-title":"Robust out-of-sample inference","volume":"99","author":"McCracken","year":"2000","journal-title":"Journal of Econometrics"},{"key":"S0266466616000426_ref9","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.econlet.2015.02.018","article-title":"Assessing point forecast accuracy by stochastic loss distance","volume":"130","author":"Diebold","year":"2015","journal-title":"Economics Letters"},{"key":"S0266466616000426_ref10","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jeconom.2003.10.019","article-title":"Optimal forecast combinations under general loss functions and forecast error distributions","volume":"122","author":"Elliott","year":"2004","journal-title":"Journal of Econometrics"},{"key":"S0266466616000426_ref1","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1017\/S0266466609100051","article-title":"Asymptotic size and a problem with subsampling and with the m out of n bootstrap","volume":"26","author":"Andrews","year":"2010","journal-title":"Econometric Theory"},{"key":"S0266466616000426_ref4","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1017\/S0266466605050498","article-title":"A test for comparing multiple misspecified conditional interval models","volume":"21","author":"Corradi","year":"2005","journal-title":"Econometric Theory"},{"key":"S0266466616000426_ref22","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1111\/j.1467-937X.2005.00350.x","article-title":"Consistent testing for stochastic dominance: A subsampling approach","volume":"72","author":"Linton","year":"2005","journal-title":"Review of Economic Studies"},{"key":"S0266466616000426_ref13","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s101080050007","article-title":"Outline of forecast theory using generalized cost functions","volume":"1","author":"Granger","year":"1999","journal-title":"Spanish Economic Review"},{"key":"S0266466616000426_ref2","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1111\/j.1475-6803.1986.tb00444.x","article-title":"Empirical analysis of the predictor of future spot rates","volume":"9","author":"Chiang","year":"1986","journal-title":"Journal of Financial Research"},{"key":"S0266466616000426_ref12","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/S0304-4076(03)00204-5","article-title":"Maximum likelihood and the bootstrap for nonlinear dynamic models","volume":"119","author":"Goncalves","year":"2004","journal-title":"Journal of Econometrics"},{"key":"S0266466616000426_ref17","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1006\/jmva.1999.1822","article-title":"Conditional empirical processes defined by nonstationary absolutely regular sequences","volume":"70","author":"Harel","year":"1999","journal-title":"Journal of Multivariate Analysis"},{"key":"S0266466616000426_ref18","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1214\/aop\/1176993379","article-title":"An invariance principle for weakly dependent sequences of random variables","volume":"12","author":"Herrndorf","year":"1984","journal-title":"Annals of Probability"},{"key":"S0266466616000426_ref7","first-page":"121","volume-title":"Causality, Prediction, and Specification Analysis: Recent Advances and Future Directions, Essays in honor of Halbert L. White, Jr","author":"Corradi","year":"2013"},{"key":"S0266466616000426_ref25","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0022-1996(83)90017-X","article-title":"Empirical exchange rate models of the seventies: Do they fit out of sample?","volume":"14","author":"Meese","year":"1983","journal-title":"Journal of International Economics"},{"key":"S0266466616000426_ref8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1080\/07350015.1995.10524599","article-title":"Comparing predictive accuracy","volume":"13","author":"Diebold","year":"1995","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466616000426_ref11","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1111\/j.1468-0262.2006.00718.x","article-title":"Tests of conditional predictive ability","volume":"74","author":"Giacomini","year":"2006","journal-title":"Econometrica"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466616000426","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T06:19:56Z","timestamp":1718864396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466616000426\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,27]]},"references-count":29,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["S0266466616000426"],"URL":"https:\/\/doi.org\/10.1017\/s0266466616000426","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,27]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2016\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}