Focused Weighted-Average Least Squares Estimator

TL;DR

The paper introduces FWALS, a computationally efficient estimator for focused model averaging that reduces complexity and performs comparably to benchmarks, especially for impulse response functions.

Contribution

We develop FWALS, a novel focused weighted-average least squares estimator that simplifies computation via semi-orthogonalization and provides theoretical and empirical performance guarantees.

Findings

FWALS closely matches the focused information criterion benchmark.

FWALS delivers stable performance for impulse response functions.

FWALS offers substantial computational savings.

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 $2^{k_2}$ 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.