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Self-weighted Estimation for Local Unit Root Regression with Applications

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Abstract

A new self-weighted least squares (LS) estimation theory is developed for local unit root (LUR) autoregression with heteroskedasticity. The proposed estimator has a mixed Gaussian limit distribution and the corresponding studentized statistic converges to a standard normal distribution free of the unknown localizing coefficient which is not consistently estimable. The estimator is super consistent with a convergence rate slightly below the OP (n) rate of LS estimation. The asymptotic theory relies on a new framework of convergence to the local time of a Gaussian process, allowing for the sample moments generated from martingales and many other integrated dependent sequences. A new unit root (UR) test in augmented autoregression is developed using self-weighted estimation and the methods are employed in predictive regression, providing an alternative approach to IVX regression. Simulation results showing good finite sample performance of these methods are reported together with a small empirical application.

Suggested Citation

  • Zhishui Hu & Nan Liu & Peter C. B. Phillips & Qiying Wang, 2024. "Self-weighted Estimation for Local Unit Root Regression with Applications," Cowles Foundation Discussion Papers 2400, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2400
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    File URL: https://cowles.yale.edu/sites/default/files/2024-07/d2400.pdf
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    Keywords

    Self-weighted least squares estimation; autoregression; super consistency; limit distribution; unit root test; predictive regression.;
    All these keywords.

    JEL classification:

    • 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

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