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The Distribution Of Rolling Regression Estimators

Author

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  • Zongwu Cai

    (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA)

  • Ted Juhl

    (School of Business, The University of Kansas, Lawrence, KS 66045, USA)

Abstract

We establish the asymptotic distribution for rolling linear regression models using various window widths. The limiting distribution depends on the width of the rolling window and on a "bias process" that is typically ignored in practice. Based on the asymptotic distribution, we tabulate critical values used to find uniform confidence intervals for the average values of regression parameters over the windows. We propose a corrected rolling regression technique that removes the bias process by rolling over smoothed parameter estimates. The procedure is illustrated using a series of Monte Carlo experiments. The paper includes an empirical example to show how the confidence bands suggest alternative conclusions about the persistence of inflation.

Suggested Citation

  • Zongwu Cai & Ted Juhl, 2020. "The Distribution Of Rolling Regression Estimators," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202218, University of Kansas, Department of Economics, revised Dec 2022.
  • Handle: RePEc:kan:wpaper:202218
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    References listed on IDEAS

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    Cited by:

    1. Jean-François Verne, 2024. "Estimating the trajectories of the Okun's coefficient and NAIRU with the rolling regression method: Evidence from Lebanon," Economics Bulletin, AccessEcon, vol. 44(1), pages 140-153.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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