Locally trimmed least squares: conventional inference in possibly nonstationary models

TL;DR

The paper introduces Locally Trimmed LS, a new IV estimation method that provides reliable inference in nonstationary and persistent data models without needing prior knowledge of the dependence structure.

Contribution

It develops a novel estimation technique that achieves conventional inference in complex, nonstationary models without requiring preliminary estimates of memory parameters.

Findings

LTLS estimators have Gaussian limit distributions in various persistence settings.

The method performs well in finite samples as shown by simulations.

Application to stock return predictability demonstrates practical usefulness.

Abstract

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.