Semiparametric testing with highly persistent predictors

We address the issue of semiparametric efficiency in bivariate regression problem with a highly persistent predictor, where joint distribution innovations is regarded an infinite-dimensional nuisance parameter. Using structural representation limit experiment and exploiting invariance relationships therein, we construct invariant point-optimal tests for coefficient interest. This approach naturally leads to family feasible based on component-wise ranks that can gain considerable power relative existing under non-Gaussian innovation distributions, while behaving equivalently Gaussianity. When i.i.d. assumption appropriate data at hand, our exploit gains possible. Moreover, show by simulation test remains well behaved some forms conditional heteroskedasticity.