A nonparametric test for the stationary density

We propose a nonparametric test for checking parametric hypotheses about the stationary density of weakly dependent observations. The test statistic is based on the L2-distance between a nonparametric and a smoothed version of a parametric estimate of the stationary density. It can be shown that this statistic behaves asymptotically as in the case of independent observations. Accordingly, we propose an i.i.d.-type bootstrap to determine the critical value for the test.