The typical predictor in predictive regressions for stock returns exhibits high persistence, which leads to nonstandard limiting distributions of the least-squares estimator and the associated t statistic. While there are several methods to deal with the issue of nonstandard distributions, the high predictor persistence also opens the door to spurious regression findings induced by the use of imperfect predictors, i.e. when the predictors do not perfectly span the conditional mean of the stock returns. To deal with such imperfect predictors, we take here a technical approach. Concretely, we robustify IVX predictive regression (Kostakis et al., 2015, Review of Financial Studies 28, 1506–1553) to the presence of smoothly varying components of the predictive system. This allows us to deal with situations where the predictors are imperfect without requiring additional knowledge on the predictive system, which is often unavailable in practice. In specific, we employ a filter which effectively employs smoothness to identify the mean component of the stock returns unaccounted for by the imperfect predictors. The limiting distribution of the resulting modified IVX t statistic is derived under sequences of local alternatives, and a wild bootstrap implementation improving the finite-sample behavior is provided. Compared to standard IVX predictive regression, there is a price to pay for such robustness in terms of power; at the same time, the IVX statistic without adjustment consistently rejects the false null of no predictability in the presence of imperfect predictors.