IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v37y2010i6p983-997.html

How to compare interpretatively different models for the conditional variance function

Author

Listed:
  • Ilmari Juutilainen
  • Juha Roning

Abstract

This study considers regression-type models with heteroscedastic Gaussian errors. The conditional variance is assumed to depend on the explanatory variables via a parametric or non-parametric variance function. The variance function has usually been selected on the basis of the log-likelihoods of fitted models. However, log-likelihood is a difficult quantity to interpret - the practical importance of differences in log-likelihoods has been difficult to assess. This study overcomes these difficulties by transforming the difference in log-likelihood to easily interpretative difference in the error of predicted deviation. In addition, methods for testing the statistical significance of the observed difference in test data log-likelihood are proposed.

Suggested Citation

  • Ilmari Juutilainen & Juha Roning, 2010. "How to compare interpretatively different models for the conditional variance function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 983-997.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:6:p:983-997
    DOI: 10.1080/02664760902984642
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760902984642
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760902984642?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Murray Aitkin, 1987. "Modelling Variance Heterogeneity in Normal Regression Using GLIM," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 332-339, November.
    2. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268, April.
    3. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    4. Dr. James Mitchell, 2005. "Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ÔfanÕ charts of inflation," National Institute of Economic and Social Research (NIESR) Discussion Papers 253, National Institute of Economic and Social Research.
    5. Jeff Fleming & Chris Kirby & Barbara Ostdiek, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
    6. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    7. Dr. James Mitchell, 2005. "Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ÔfanÕ charts of inflation," National Institute of Economic and Social Research (NIESR) Discussion Papers 253, National Institute of Economic and Social Research.
    8. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    9. James Mitchell & Stephen G. Hall, 2005. "Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ‘Fan’ Charts of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 995-1033, December.
    10. 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.
    11. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
    Full references (including those not matched with items on IDEAS)

    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. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    2. 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.
    3. Berg, Tim O. & Henzel, Steffen R., 2015. "Point and density forecasts for the euro area using Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1067-1095.
    4. Manzan, Sebastiano & Zerom, Dawit, 2013. "Are macroeconomic variables useful for forecasting the distribution of U.S. inflation?," International Journal of Forecasting, Elsevier, vol. 29(3), pages 469-478.
    5. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    6. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2010. "Combining predictive densities using Bayesian filtering with applications to US economics data," Working Paper 2010/29, Norges Bank.
    7. Barbara Rossi, 2021. "Forecasting in the Presence of Instabilities: How We Know Whether Models Predict Well and How to Improve Them," Journal of Economic Literature, American Economic Association, vol. 59(4), pages 1135-1190, December.
    8. Tae-Hwy Lee & Yong Bao & Burak Saltoğlu, 2007. "Comparing density forecast models Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003; see Bao et al. (2004)," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 203-225.
    9. Tommaso Proietti & Martyna Marczak & Gianluigi Mazzi, 2017. "Euromind‐ D : A Density Estimate of Monthly Gross Domestic Product for the Euro Area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(3), pages 683-703, April.
    10. Marcus P. A. Cobb, 2020. "Aggregate density forecasting from disaggregate components using Bayesian VARs," Empirical Economics, Springer, vol. 58(1), pages 287-312, January.
    11. Labonne, Paul, 2025. "Asymmetric uncertainty: Nowcasting using skewness in real-time data," International Journal of Forecasting, Elsevier, vol. 41(1), pages 229-250.
    12. Diks, Cees & Panchenko, Valentyn & Sokolinskiy, Oleg & van Dijk, Dick, 2014. "Comparing the accuracy of multivariate density forecasts in selected regions of the copula support," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 79-94.
    13. Paulo Mauricio S�nchez Beltr�n & Luis Fernando Melo Velandia, 2013. "Combinaci�n de brechas del producto colombiano," Borradores de Economia 10973, Banco de la Republica.
    14. Paul Labonne, 2022. "Asymmetric Uncertainty: Nowcasting Using Skewness in Real-time Data," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2022-23, Economic Statistics Centre of Excellence (ESCoE).
    15. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    16. Peter McAdam & Anders Warne, 2024. "Density forecast combinations: The real‐time dimension," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1153-1172, August.
    17. Ricardo Crisóstomo & Lorena Couso, 2018. "Financial density forecasts: A comprehensive comparison of risk‐neutral and historical schemes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(5), pages 589-603, August.
    18. Cees Diks & Valentyn Panchenko & Oleg Sokolinskiy, & Dick van Dijk, 2013. "Comparing the Accuracy of Copula-Based Multivariate Density Forecasts in Selected Regions of Support," Tinbergen Institute Discussion Papers 13-061/III, Tinbergen Institute.
    19. Marc-Oliver Pohle, 2020. "The Murphy Decomposition and the Calibration-Resolution Principle: A New Perspective on Forecast Evaluation," Papers 2005.01835, arXiv.org.
    20. Ana Beatriz Galvão & James Mitchell, 2019. "Measuring Data Uncertainty: An Application using the Bank of England's "Fan Charts" for Historical GDP Growth," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2019-08, Economic Statistics Centre of Excellence (ESCoE).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:taf:japsta:v:37:y:2010:i:6:p:983-997. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.