How to compare interpretatively different models for the conditional variance function

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.

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