Using the dependent wild bootstrap for the nonparametric goodness-of-fit test for density functions

In this paper, we consider the well-known nonparametric consistent model-specification test for the stationary density function (see [Ait-Sahalia Y. Testing continuous-time models of the spot interest rate. Rev Financ Stud. 1996;9:385-426; Li Q. Nonparametric testing of closeness between two unknown distribution functions. Econ Rev. 1996;15:261-274; Fan Y, Ullah A. On goodness-of-fit tests for weakly dependent processes using kernel method. J Nonparametric Stat. 2000;11:337-360]) and reinvestigate it carefully using asymptotics and simulation. Our work reveals that the test is subject to power and size distortions, which are mainly caused by dependence or convergence rate changes under the null and alternative hypothesis. A dependent wild bootstrap is newly suggested as a feasible remedy to such distortions. Our result provides a complete explanation as well as a solution to the problem that experienced by Ait-Sahalia [Testing continuous-time models of the spot interest rate. Rev Financ Stud. 1996;9:385-426], that is, that the test rejects true models too often when independent and identically distributed asymptotic critical values are used.