[go: up one dir, main page]

IDEAS home Printed from https://ideas.repec.org/p/rut/rutres/201502.html
   My bibliography  Save this paper

Robust Forecast Comparison

Author

Listed:
  • Sainan Jin

    (Singapore Management University)

  • Valentina Corradi

    (University of Surrey)

  • Norman Swanson

    (Rutgers University)

Abstract
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. This paper addresses this issue by using a novel criterion for forecast evaluation which is based on the entire distribution of forecast errors. We introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority, and we establish a mapping between GL (CL) superiority and first (second) order stochastic dominance. This allows us to develop a forecast evaluation procedure based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi and Whang (2005). The asymptotic null distributions of our test statistics are nonstandard, and resampling procedures are used to obtain the critical values. Additionally, the tests are consistent and have nontrivial local power under a sequence of local alternatives. In addition to the stationary case, we outline theory extending our tests to the case of heterogeneity induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples; and an application to exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.

Suggested Citation

  • Sainan Jin & Valentina Corradi & Norman Swanson, 2015. "Robust Forecast Comparison," Departmental Working Papers 201502, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201502
    as

    Download full text from publisher

    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2015-02.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    2. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    3. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    4. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    5. Harel, Michel & Puri, Madan L., 1999. "Conditional Empirical Processes Defined by Nonstationary Absolutely Regular Sequences," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 250-285, August.
    6. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    7. Raffaella Giacomini & Barbara Rossi, 2009. "Detecting and Predicting Forecast Breakdowns," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(2), pages 669-705.
    8. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    9. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    10. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    11. Ryan Sullivan & Allan Timmermann & Halbert White, 1999. "Data‐Snooping, Technical Trading Rule Performance, and the Bootstrap," Journal of Finance, American Finance Association, vol. 54(5), pages 1647-1691, October.
    12. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    13. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 3, pages 99-134, Elsevier.
    14. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    15. Clive W.J. Granger, 1999. "Outline of forecast theory using generalized cost functions," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 161-173.
    16. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    17. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    18. Peter Hansen, 2003. "Asymptotic Tests of Composite Hypotheses," Working Papers 2003-09, Brown University, Department of Economics.
    19. Elliott, Graham & Gargano, Antonio & Timmermann, Allan, 2013. "Complete subset regressions," Journal of Econometrics, Elsevier, vol. 177(2), pages 357-373.
    20. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    21. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    22. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-840, November.
    23. Francis X. Diebold & Minchul Shin, 2017. "Assessing point forecast accuracy by stochastic error distance," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 588-598, October.
    24. Clements, Michael P. & Hendry, David F. (ed.), 2011. "The Oxford Handbook of Economic Forecasting," OUP Catalogue, Oxford University Press, number 9780195398649.
    25. Atsushi Inoue & Lutz Kilian, 2005. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 371-402.
    26. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    27. Diebold, Francis X. & Shin, Minchul, 2015. "Assessing point forecast accuracy by stochastic loss distance," Economics Letters, Elsevier, vol. 130(C), pages 37-38.
    28. Hansen, Bruce E., 1996. "Stochastic Equicontinuity for Unbounded Dependent Heterogeneous Arrays," Econometric Theory, Cambridge University Press, vol. 12(2), pages 347-359, June.
    29. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    30. Elliott, Graham & Timmermann, Allan, 2002. "Optimal Forecast Combination Under General Loss Functions and Forecast Error Distributions," University of California at San Diego, Economics Working Paper Series qt15r9t2q2, Department of Economics, UC San Diego.
    31. Granger,Clive W. J., 1999. "Empirical Modeling in Economics," Cambridge Books, Cambridge University Press, number 9780521662086, September.
    32. Xiaohong Chen & Norman R. Swanson (ed.), 2013. "Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis," Springer Books, Springer, edition 127, number 978-1-4614-1653-1, December.
    33. Goncalves, Silvia & White, Halbert, 2004. "Maximum likelihood and the bootstrap for nonlinear dynamic models," Journal of Econometrics, Elsevier, vol. 119(1), pages 199-219, March.
    34. Thomas C. Chiang, 1986. "Empirical Analysis On The Predictors Of Future Spot Rates," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 9(2), pages 153-162, June.
    35. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    36. Chao, John & Corradi, Valentina & Swanson, Norman R., 2001. "Out-Of-Sample Tests For Granger Causality," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 598-620, September.
    37. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October.
    38. Granger, Clive W.J. & Machina, Mark J., 2006. "Forecasting and Decision Theory," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 2, pages 81-98, Elsevier.
    39. Frankel, Jeffrey A. & Rose, Andrew K., 1995. "Empirical research on nominal exchange rates," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 33, pages 1689-1729, Elsevier.
    40. Donald W.K. Andrews, 2011. "Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power," Cowles Foundation Discussion Papers 1815, Cowles Foundation for Research in Economics, Yale University.
    41. Corradi, Valentina & Swanson, Norman R., 2005. "A Test For Comparing Multiple Misspecified Conditional Interval Models," Econometric Theory, Cambridge University Press, vol. 21(5), pages 991-1016, October.
    42. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
    43. repec:bla:jfinan:v:43:y:1988:i:4:p:933-48 is not listed on IDEAS
    44. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
    45. G. Elliott & C. Granger & A. Timmermann (ed.), 2013. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 2, number 2.
    46. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
    47. William C. Hunter & Stephen G. Timme, 1992. "A Stochastic Dominance Approach to Evaluating Foreign Exchange Hedging Strategies," Financial Management, Financial Management Association, vol. 21(3), Fall.
    48. Valentina Corradi & Norman Swanson, 2013. "A Survey of Recent Advances in Forecast Accuracy Comparison Testing, with an Extension to Stochastic Dominance," Departmental Working Papers 201309, Rutgers University, Department of Economics.
    49. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    50. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    51. Meese, R. & Rogoff, K., 1988. "Was It Real? The Exchange Rate-Interest Differential Ralation Over The Modern Floating-Rate Period," Working papers 368, Wisconsin Madison - Social Systems.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Francis X. Diebold & Minchul Shin, 2017. "Assessing point forecast accuracy by stochastic error distance," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 588-598, October.
    2. Arvanitis, Stelios & Post, Thierry & Potì, Valerio & Karabati, Selcuk, 2021. "Nonparametric tests for Optimal Predictive Ability," International Journal of Forecasting, Elsevier, vol. 37(2), pages 881-898.
    3. Post, Thierry & Karabatı, Selçuk & Arvanitis, Stelios, 2019. "Robust optimization of forecast combinations," International Journal of Forecasting, Elsevier, vol. 35(3), pages 910-926.
    4. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    5. Anghel, Dan Gabriel, 2021. "Data Snooping Bias in Tests of the Relative Performance of Multiple Forecasting Models," Journal of Banking & Finance, Elsevier, vol. 126(C).
    6. Sander Barendse & Andrew J. Patton, 2022. "Comparing Predictive Accuracy in the Presence of a Loss Function Shape Parameter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1057-1069, June.
    7. Mehmet Pinar & Thanasis Stengos & Nikolas Topaloglou, 2022. "Stochastic dominance spanning and augmenting the human development index with institutional quality," Annals of Operations Research, Springer, vol. 315(1), pages 341-369, August.
    8. Valentina Corradi & Sainan Jin & Norman R. Swanson, 2023. "Robust forecast superiority testing with an application to assessing pools of expert forecasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 596-622, June.
    9. Anyfantaki, Sofia & Arvanitis, Stelios & Topaloglou, Nikolas, 2021. "Diversification benefits in the cryptocurrency market under mild explosivity," European Journal of Operational Research, Elsevier, vol. 295(1), pages 378-393.
    10. Yen, Yu-Min & Yen, Tso-Jung, 2021. "Testing forecast accuracy of expectiles and quantiles with the extremal consistent loss functions," International Journal of Forecasting, Elsevier, vol. 37(2), pages 733-758.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    2. Raffaella Giacomini & Barbara Rossi, 2013. "Forecasting in macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 17, pages 381-408, Edward Elgar Publishing.
    3. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    4. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    5. Valentina Corradi & Norman Swanson, 2013. "A Survey of Recent Advances in Forecast Accuracy Comparison Testing, with an Extension to Stochastic Dominance," Departmental Working Papers 201309, Rutgers University, Department of Economics.
    6. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 3, pages 99-134, Elsevier.
    7. Valentina Corradi & Sainan Jin & Norman R. Swanson, 2023. "Robust forecast superiority testing with an application to assessing pools of expert forecasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 596-622, June.
    8. Rapach, David & Zhou, Guofu, 2013. "Forecasting Stock Returns," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 328-383, Elsevier.
    9. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    10. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    11. Dichtl, Hubert & Drobetz, Wolfgang & Neuhierl, Andreas & Wendt, Viktoria-Sophie, 2021. "Data snooping in equity premium prediction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 72-94.
    12. Graham Elliott & Allan Timmermann, 2016. "Forecasting in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 81-110, October.
    13. Valentina Corradi & Norman Swanson, 2004. "Bootstrap Procedures for Recursive Estimation Schemes With Applications to Forecast Model Selection," Departmental Working Papers 200418, Rutgers University, Department of Economics.
    14. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    15. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228.
    16. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    17. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    18. Li, Jia & Patton, Andrew J., 2018. "Asymptotic inference about predictive accuracy using high frequency data," Journal of Econometrics, Elsevier, vol. 203(2), pages 223-240.
    19. Granziera, Eleonora & Hubrich, Kirstin & Moon, Hyungsik Roger, 2014. "A predictability test for a small number of nested models," Journal of Econometrics, Elsevier, vol. 182(1), pages 174-185.
    20. Todd E. Clark & Michael W. McCracken, 2010. "Testing for unconditional predictive ability," Working Papers 2010-031, Federal Reserve Bank of St. Louis.

    More about this item

    Keywords

    convex loss function; empirical processes; forecast superiority; general loss function;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rut:rutres:201502. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/derutus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.