  We propose pair copula constructed point-optimal sign tests in the context of
linear and nonlinear predictive regressions with endogenous, persistent
regressors, and disturbances exhibiting serial (nonlinear) dependence. The
proposed approach entails considering the entire dependence structure of the
signs to capture the serial dependence, and building feasible test statistics
based on pair copula constructions of the sign process. The tests are exact and
valid in the presence of heavy tailed and nonstandard errors, as well as
heterogeneous and persistent volatility. Furthermore, they may be inverted to
build confidence regions for the parameters of the regression function.
Finally, we adopt an adaptive approach based on the split-sample technique to
maximize the power of the test by finding an appropriate alternative
hypothesis. In a Monte Carlo study, we compare the performance of the proposed
"quasi"-point-optimal sign tests based on pair copula constructions by
comparing its size and power to those of certain existing tests that are
intended to be robust against heteroskedasticity. The simulation results
maintain the superiority of our procedures to existing popular tests.
