[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/syb/wpbsba/2123-27307.html
   My bibliography  Save this paper

On the uncertainty of a combined forecast: The critical role of correlation

Author

Listed:
  • Magnus, Jan
  • Vasnev, Andrey
Abstract
The purpose of this paper is to show that the effect of the zero-correlation assumption in combining forecasts can be huge, and that ignoring (positive) correlation can lead to confidence bands around the forecast combination that are much too narrow. In the typical case where three or more forecasts are combined, the estimated variance increases without bound when correlation increases. Intuitively, this is because similar forecasts provide little information if we know that they are highly correlated. Although we concentrate on forecast combinations and confidence bands, our theory applies to any statistic where the observations are linearly combined. We apply our theoretical results to explain why forecasts by Central Banks (in our case, the Bank of Japan) are so frequently misleadingly precise. In most cases, a correlation above 0.7 is required to produce reasonable confidence bands.

Suggested Citation

  • Magnus, Jan & Vasnev, Andrey, 2021. "On the uncertainty of a combined forecast: The critical role of correlation," Working Papers BAWP-2022-01, University of Sydney Business School, Discipline of Business Analytics.
    • Handle: RePEc:syb:wpbsba:2123/27307
    as

    Download full text from publisher

    File URL: https://hdl.handle.net/2123/27307
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Meira, Erick & Cyrino Oliveira, Fernando Luiz & Jeon, Jooyoung, 2021. "Treating and Pruning: New approaches to forecasting model selection and combination using prediction intervals," International Journal of Forecasting, Elsevier, vol. 37(2), pages 547-568.
    2. Xiaoqian Wang & Yanfei Kang & Fotios Petropoulos & Feng Li, 2022. "The uncertainty estimation of feature-based forecast combinations," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(5), pages 979-993, May.
    3. 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.
    4. 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.
    5. Hounyo, Ulrich & Lahiri, Kajal, 2023. "Estimating the variance of a combined forecast: Bootstrap-based approach," Journal of Econometrics, Elsevier, vol. 232(2), pages 445-468.
    6. Qian, Wei & Rolling, Craig A. & Cheng, Gang & Yang, Yuhong, 2022. "Combining forecasts for universally optimal performance," International Journal of Forecasting, Elsevier, vol. 38(1), pages 193-208.
    7. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2018. "The M4 Competition: Results, findings, conclusion and way forward," International Journal of Forecasting, Elsevier, vol. 34(4), pages 802-808.
    8. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    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. Ikefuji, Masako & Magnus, Jan R. & Vasnev, Andrey L., 2023. "The role of data and priors in estimating climate sensitivity," Working Papers BAWP-2023-02, University of Sydney Business School, Discipline of Business Analytics.
    2. Thompson, Ryan & Qian, Yilin & Vasnev, Andrey L., 2024. "Flexible global forecast combinations," Omega, Elsevier, vol. 126(C).
    3. Astafyeva, Ekaterina & Turuntseva, Marina, 2024. "Forecast evaluation improving using the simplest methods of individual forecasts’ combination," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 74, pages 78-103.

    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. Salinas, David & Flunkert, Valentin & Gasthaus, Jan & Januschowski, Tim, 2020. "DeepAR: Probabilistic forecasting with autoregressive recurrent networks," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1181-1191.
    2. Diebold, Francis X. & Shin, Minchul & Zhang, Boyuan, 2023. "On the aggregation of probability assessments: Regularized mixtures of predictive densities for Eurozone inflation and real interest rates," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Lu, Xinjie & Ma, Feng & Xu, Jin & Zhang, Zehui, 2022. "Oil futures volatility predictability: New evidence based on machine learning models11All the authors contribute to the paper equally," International Review of Financial Analysis, Elsevier, vol. 83(C).
    4. Godahewa, Rakshitha & Bergmeir, Christoph & Webb, Geoffrey I. & Montero-Manso, Pablo, 2023. "An accurate and fully-automated ensemble model for weekly time series forecasting," International Journal of Forecasting, Elsevier, vol. 39(2), pages 641-658.
    5. Dan Zhu & Qingwei Wang & John Goddard, 2022. "A new hedging hypothesis regarding prediction interval formation in stock price forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 697-717, July.
    6. Davide Pettenuzzo & Francesco Ravazzolo, 2016. "Optimal Portfolio Choice Under Decision‐Based Model Combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1312-1332, November.
    7. Baumeister, Christiane & Kilian, Lutz & Lee, Thomas K., 2014. "Are there gains from pooling real-time oil price forecasts?," Energy Economics, Elsevier, vol. 46(S1), pages 33-43.
    8. Brave, Scott A. & Gascon, Charles & Kluender, William & Walstrum, Thomas, 2021. "Predicting benchmarked US state employment data in real time," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1261-1275.
    9. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    10. Fernando M. Duarte & Carlo Rosa, 2015. "The equity risk premium: a review of models," Economic Policy Review, Federal Reserve Bank of New York, issue 2, pages 39-57.
    11. Bakalli, Gaetan & Guerrier, Stéphane & Scaillet, Olivier, 2023. "A penalized two-pass regression to predict stock returns with time-varying risk premia," Journal of Econometrics, Elsevier, vol. 237(2).
    12. Uniejewski, Bartosz & Maciejowska, Katarzyna, 2023. "LASSO principal component averaging: A fully automated approach for point forecast pooling," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1839-1852.
    13. Yi, Yongsheng & Ma, Feng & Zhang, Yaojie & Huang, Dengshi, 2019. "Forecasting stock returns with cycle-decomposed predictors," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 250-261.
    14. Lyócsa, Štefan & Molnár, Peter & Todorova, Neda, 2017. "Volatility forecasting of non-ferrous metal futures: Covariances, covariates or combinations?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 51(C), pages 228-247.
    15. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    16. Mauro Costantini & Ulrich Gunter & Robert M. Kunst, 2017. "Forecast Combinations in a DSGE‐VAR Lab," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(3), pages 305-324, April.
    17. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    18. Ferrara, Laurent & Marsilli, Clément & Ortega, Juan-Pablo, 2014. "Forecasting growth during the Great Recession: is financial volatility the missing ingredient?," Economic Modelling, Elsevier, vol. 36(C), pages 44-50.
    19. Paroissien, Emmanuel, 2020. "Forecasting bulk prices of Bordeaux wines using leading indicators," International Journal of Forecasting, Elsevier, vol. 36(2), pages 292-309.
    20. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.

    More about this item

    Keywords

    Combining information; Correlation; Growth forecasting; Inflation forecasting; Central Banks;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

    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:syb:wpbsba:2123/27307. 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: Artem Prokhorov (email available below). General contact details of provider: https://edirc.repec.org/data/sbsydau.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.