Jiajing Sun

Jiajing Sun

PhD, CFA charterholder, FIMA, Member of the London Mathematical Society. Associate Professor and the Deputy Director of the Department of Statistics and Data Science, School of Economics and Management, University of the Chinese Academy of Sciences.

Adjusted-Range Self-Normalization for Asymptotically Linear Time-Series Estimators

Published:

This working paper develops adjusted-range self-normalization for asymptotically linear time-series estimators. The approach normalizes the endpoint estimation error by the range of a centered influence-function partial-sum bridge, so the unknown long-run scale cancels under a scalar functional central limit theorem.

Authors:

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

Summary and Contribution:

The paper provides a tuning-free path-functional approach to inference for time-series estimators that admit asymptotically linear representations. It develops feasible implementations based on estimated influence-function contributions and recursive estimators, reports analytic scalar critical values, and gives primitive verification for OLS and smooth GMM.

For vector targets, the paper introduces an affine-equivariant range-body construction based on the convex hull of bridge increments and its Minkowski gauge. This extension avoids coordinate-by-coordinate scalarization and preserves invariance under nonsingular reparameterizations.

Evidence and Applications:

Simulation evidence documents the central coverage-length and size-power trade-offs. Adjusted-range inference can deliver shorter intervals and stronger power than Shao-type self-normalization in score martingale-difference designs, while persistent designs can create coverage costs.

The empirical work includes a public score-based application using Survey of Professional Forecasters bin-probability reweighting. Supplementary checks report a predictive-regression illustration and robustness diagnostics using public Fama-French and FRED data.

Keywords:

Adjusted range; self-normalization; confidence interval; hypothesis testing; long-run variance; OLS; GMM; time-series econometrics.

Recommended citation: Hong, Y., Lin, Z., Linton, O., Newey, W. K., & Sun, J. (2026). Adjusted-Range Self-Normalization for Asymptotically Linear Time-Series Estimators. Working paper.