Affine-Equivariant Adjusted-Range Self-Normalization

Yongmiao Hong, Zhuo Lin, Oliver B. Linton, Whitney K. Newey and Jiajing Sun

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

Abstract: We propose affine-equivariant adjusted-range self-normalization for joint inference on time-series parameters. The method uses the projected ranges of a centered influence path to normalize estimation error, yielding pivotal limiting inference without estimating the long-run covariance matrix. The resulting statistic is invariant to nonsingular linear reparameterizations, and its inversion yields affine-equivariant confidence regions. In the univariate case, the proposed method reduces exactly to adjusted-range self-normalization. We derive scalar reference distributions and accommodate proportional variance accumulation through appropriate path centering. Simulations show power gains over quadratic self-normalization and quantify size distortions under persistent dependence. An application to U.S. fiscal multipliers illustrates joint inference across horizons and its sensitivity to concentrated identifying variation.

Keywords: Self-Normalized Inference; Long-Run Covariance; Affine Equivariance; Influence Functions; Local Projections (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 C32 (search for similar items in EconPapers)
Date: 2026-09-08
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:2678

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