Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root
AbstractAsymptotic expansions are employed in a dynamic regression model with a unit root in order to find approximations for the bias, the variance and for the mean squared error of the least-squares estimator. For this purpose such expansions are shown to be useful only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. It is found that large sample and small disturbance asymptotic techniques give closely related results in this model, which is not the case in stable dynamic regression models. The results are specialised to the random walk with drift model, where it is seen that the ratio of the standard deviation of the disturbance tot he drift term plays a crucial role. The random walk to the model with drift plus a linear trend is also examined. The accuracy of the approximations are checked in the context of these models making use of a set of Monte Carlo experiments to estimate the true moments.
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Bibliographic InfoPaper provided by Exeter University, Department of Economics in its series Discussion Papers with number 9909.
Length: 30 pages
Date of creation: 1998
Date of revision:
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ESTIMATOR ; TIME SERIES ; REGRESSION ANALYSIS;
Other versions of this item:
- Jan F. Kiviet & Garry D.A. Phillips, 2001. "Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root," Tinbergen Institute Discussion Papers 01-118/4, Tinbergen Institute.
- 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 &bull Diffusion Processes
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- Pesaran, M.H. & Timmermann, A., 2003.
"Small Sample Properties of Forecasts from Autoregressive Models under Structural Breaks,"
Cambridge Working Papers in Economics
0331, Faculty of Economics, University of Cambridge.
- Pesaran, M. Hashem & Timmermann, Allan, 2005. "Small sample properties of forecasts from autoregressive models under structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 183-217.
- Allan Timmermann & M. Hashem Pesaran, 2003. "Small Sample Properties of Forecasts from Autoregressive Models under Structural Breaks," CESifo Working Paper Series 990, CESifo Group Munich.
- Pesaran, M Hashem & Timmermann, Allan G, 2004. "Small Sample Properties of Forecasts From Autoregressive Models Under Structural Breaks," CEPR Discussion Papers 4401, C.E.P.R. Discussion Papers.
- Liu-Evans, Gareth, 2010. "An alternative approach to approximating the moments of least squares estimators," MPRA Paper 26550, University Library of Munich, Germany.
- Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.
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