Advances and Applications in Statistics
Volume 36, Issue 2, Pages 105 - 118
(October 2013)
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SADDLEPOINT APPROXIMATIONS FOR THE ESTIMATOR ON A LAGGED DEPENDENT VARIABLE
Patrick Marsh
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Abstract: The estimator of the coefficient on a lagged dependent variable in the linear regression model is known to be a ratio of non-central quadratic forms. This paper provides a saddlepoint approximation for its finite sample density and distribution, under the assumption of Gaussian errors. By providing an explicit asymptotic order of error for the approximation, its inferential and methodological usefulness is significantly extended. Asymptotically the approximation remains valid under more general error assumptions and, crucially, upon consistent estimation of the noncentrality. Numerical experiments demonstrate the high accuracy of the approximation. |
Keywords and phrases: autoregression, saddlepoint approximation, lagged dependent variable. |
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