  A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is
developed which yields estimators with (mixed) Gaussian limit distributions in
situations where the data may be weakly or strongly persistent. In particular,
we allow for nonlinear predictive type of regressions where the regressor can
be stationary short/long memory as well as nonstationary long memory process or
a nearly integrated array. The resultant t-tests have conventional limit
distributions (i.e. N(0; 1)) free of (near to unity and long memory) nuisance
parameters. In the case where the regressor is a fractional process, no
preliminary estimator for the memory parameter is required. Therefore, the
practitioner can conduct inference while being agnostic about the exact
dependence structure in the data. The LTLS estimator is obtained by applying
certain chronological trimming to the OLS instrument via the utilisation of
appropriate kernel functions of time trend variables. The finite sample
performance of LTLS based t-tests is investigated with the aid of a simulation
experiment. An empirical application to the predictability of stock returns is
also provided.
