Abstract

This paper proposes a method for comparing and combining conditional quantile forecasts in an out-of-sample framework. We construct a Conditional Quantile Forecast Encompassing (CQFE) test as a Wald-type test of superior predictive ability. Rejection of CQFE provides a basis for combination of conditional quantile forecasts. Central features of our encompassing test are: (1) the use of the ‘tick ’ loss function; (2) a conditional, ratherthanunconditional approach to out-of-sample evaluation, and, (3) the derivation of our test in an environment with non-vanishing estimation uncertainty. Some of the advantages of our approach are that it allows the forecasts to be generated by using general estimation procedures and that it is applicable when the forecasts are based on both nested and non-nested models. The test is also relatively easy to implement using standard GMM techniques. An empirical application to Value-at-Risk evaluation illustrates the usefulness of our method.

Citations