Self-weighted Estimation for Local Unit Root Regression with Applications

Zhishui Hu, Nan Liu, Peter Phillips and Qiying Wang
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Zhishui Hu: University of Science and Technology of China
Nan Liu: Xiamen University
Qiying Wang: University of Sydney

No 2400, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Self-weighted least squares estimation; autoregression; super consistency; limit distribution; unit root test; predictive regression. (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2024-04
New Economics Papers: this item is included in nep-ecm and nep-ets
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