Variational Bayes for assessment of dynamic quantile forecasts

Recently, various Bayes factor analogues of frequentist tests for the accuracy of dynamic quantile forecasts have been developed. However, in evaluating the marginal likelihoods involved, either inappropriate assumptions have been made, or pre-packaged multivariate adaptive quadrature methods have been employed, without an accuracy assessment. This paper develops variational Bayes methods for estimating lower bounds for these marginal likelihoods efficiently. This facilitates a more accurate version of one existing Bayesian test, and allows for the development of a new test based on the probit regression model. The size and power properties of the proposed methods are examined via a simulation study, illustrating favourable comparisons with existing testing methods. The accuracy and speed of the VB methods are also assessed. An empirical study illustrates the sensible performance and applicability of the proposed methods, relative to standard tests, for assessing the adequacy of a range of forecast models for the Value at Risk (VaR) in several financial market data series.