Evaluation and Combination of Conditional Quantile Forecasts
This paper proposes a method for comparing and combining conditional quantile forecasts based on the principle of 'encompassing'. Our test for conditional quantile forecast encompassing (CQFE) is a test of superior predictive ability, constructed as a Wald-type test on the coefficients of an optimal combination of alternative forecasts. The CQFE test is a 'model free' test that can be used to compare any given number of alternative forecasts, and is relatively easy to implement by GMM techniques appropriately modified to accommodate non-differentiable criterion functions. Further, our theoretical framework provides a basis for combining quantile forecasts, when neither forecast has superior predictive ability. A central feature of our method is the focus on conditional, rather than unconditional expected loss in the formulation of the encompassing test, which links our approach to Christoffersen's (1998) 'conditional coverage' test for evaluation of quantile forecasts. An empirical application to the problem of Value at Risk evaluation illustrates the usefulness of the proposed techniques.
encompassing, forcast combination, loss function, value at risk, GMM,
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. Two central features of our implementation of the principle of encompassing are, first, the use of the 'tick' loss function and, second, a conditional, rather than unconditional approach to out-of-sample evaluation. Some of the advantages of the conditional 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.
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