Moment Approximation for Least-Squares Estimator in First-Order Regression Models with Unit Root and Nonnormal Errors

Yong Bao, Aman Ullah and Ru Zhang

A chapter in Essays in Honor of Peter C. B. Phillips, 2014, vol. 14, pp 65-92 from Emerald Group Publishing Limited

Abstract: An extensive literature in econometrics focuses on finding the exact and approximate first and second moments of the least-squares estimator in the stable first-order linear autoregressive model with normally distributed errors. Recently,Kiviet and Phillips (2005)developed approximate moments for the linear autoregressive model with a unit root and normally distributed errors. An objective of this paper is to analyze moments of the estimator in the first-order autoregressive model with a unit root and nonnormal errors. In particular, we develop new analytical approximations for the first two moments in terms of model parameters and the distribution parameters. Through Monte Carlo simulations, we find that our approximate formula perform quite well across different distribution specifications in small samples. However, when the noise to signal ratio is huge, bias distortion can be quite substantial, and our approximations do not fare well.

Keywords: Unit root; nonnormal; moment approximation; C22; C20; C13 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-905320140000033003

DOI: 10.1108/S0731-905320140000033003

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