Focused Weighted-Average Least Squares Estimator

Abstract: We propose a focused weighted-average least squares (FWALS) estimator that addresses the computational burden of focused model averaging. By semi-orthogonalizing auxiliary regressors, the weighting problem is reduced from $2<sup>{k_2}$ sub-models to at most $k_2$ regressor-wise weights, yielding a tractable sub-optimal procedure. Under local-to-zero conditions, we derive the limiting distribution of FWALS for smooth focused functions and provide a plug-in AMSE criterion for data-driven weight selection. Simulations show that FWALS closely matches the focused information criterion (FIC) benchmark and delivers stable performance when focused function is designed for impulse response function. Prior-based WALS can be competitive in some settings, but its performance depends on the signal regime and the design of focused parameter. Overall, FWALS offers a practical and robust alternative with substantial computational savings.