A new class of independence tests for interval forecasts evaluation

Interval forecasts evaluation can be reduced to examining the unconditional coverage and independence properties of the hit sequence. A new class of exact independence tests for the hit sequence and a definition for tendency to clustering of violations are proposed. The tests are suitable for detecting models with a tendency to generate clusters of violations and are based on an exact distribution that does not depend on an unknown parameter. The asymptotic distribution is also derived. The choice of one test within the class is studied. Moreover, a simulation study provides evidence that, in order to test the independence hypothesis, the suggested tests perform better than other tests presented in the literature. An empirical application is given for a period that includes the 2008 financial crisis.