Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models
AbstractAn approximation to order T−2 is obtained for the bias of the full vector of least-squares estimates obtained from a sample of size T in general stable but not necessarily stationary ARX(1) models with normal disturbances. This yields generalizations, allowing for various forms of initial conditions, of Kendall’s and White’s classic results for stationary AR(1) models. The accuracy of various alternative approximations is examined and compared by simulation for particular parameterizations of AR(1) and ARX(1) models. The results show that often the second-order approximation is considerably better than its first-order counterpart and hence opens up perspectives for improved bias correction. However, order T−2 approximations are also found to be more vulnerable in the near unit root case than the much simpler order T−1 approximations.
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Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 11 ()
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Web page: http://www.elsevier.com/locate/csda
ARX-model; Asymptotic expansion; Bias approximation; Lagged dependent variable; Monte Carlo simulation;
Other versions of this item:
- Kiviet, J.F. & Phillips, G.D.A., 1999. "Higher-Order Asymptotic Expansions of the Least-Squares Estimation Bias in First-Order Dynamic Regression Models," Discussion Papers 9903, Exeter University, Department of Economics.
- 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
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- Jan F. KIVIET & Garry D.A. PHILLIPS, 2012. "Improved Variance Estimation of Maximum Likelihood Estimators in Stable First-Order Dynamic Regression Models," Economic Growth centre Working Paper Series 1206, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre.
- Jan F. Kiviet & Garry D. A. Phillips, 2000. "Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models," Econometric Society World Congress 2000 Contributed Papers 0631, Econometric Society.
- Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
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