Calculating the Distribution of the Serial Correlation Estimator by Saddlepoint Integration

Carl W. Helstrom

Econometric Theory, 1996, vol. 12, issue 3, 458-480

Abstract: The efficient method of numerical saddlepoint integration is described and applied to calculating the probability distribution of the maximum likelihood and Yule-Walker estimators of the correlation coefficient a of a first-order autoregressive normal time series with initial value either zero or nonzero when a finite number n of data are at hand. Stationary time series of the same type are also treated. Significance points are computed in a number of examples to show how, as n increases, the finite-sample distributions approach the asymptotic distributions that have appeared in the literature.

Date: 1996
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