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The Distribution Of Rolling Regression Estimators

Author

Listed:
  • 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 find the asymptotic distribution for rolling linear regression models various window widths. The limiting distribution depends on using the width of the rolling window, and on a “bias process†that is typically ignored in practice. Based on the 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 the 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 202013, University of Kansas, Department of Economics, revised Aug 2020.
    • Handle: RePEc:kan:wpaper:202013
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    File URL: http://www2.ku.edu/~kuwpaper/2020Papers/202013.pdf
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    More about this item

    Keywords

    Asymptotic distribution; Bias correction; Nonparametric estimation; Rolling regressions; Time-varying parameters.;
    All these keywords.

    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

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