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Affine-Equivariant Adjusted-Range Self-Normalization

Author

Listed:
  • Hong, Y.
  • Lin, Z.
  • Linton, O. B.
  • Newey, W. K.
  • Sun, J.

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.

Suggested Citation

  • Hong, Y. & Lin, Z. & Linton, O. B. & Newey, W. K. & Sun, J., 2026. "Affine-Equivariant Adjusted-Range Self-Normalization," Cambridge Working Papers in Economics 2678, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2678
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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