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How to compare interpretatively different models for the conditional variance function

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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.
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