Advances and Applications in Statistics
Volume 13, Issue 2, Pages 131 - 164
(December 2009)
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AN INVERTED BETA APPROXIMATION TO A MPI UNIT ROOT TEST
Aránzazu De Juan (Spain) and Antonio S. M. Arroyo (Spain)
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Abstract: We extend a result of Wood [38] to a random linear combination of chi-squared variables. The statistic being studied is King’s [22] small-sample, pointwise, most powerful, and invariant (MPI) test of spherically symmetric versus elliptically symmetric distributions in a unit root context. References to the latter are Sargan and Bhargava [31], Bhargava [1, 2], and Shively [34]. With no need either for iterative, numerical inversion of the characteristic function or asymptotic theory, the added value of our paper is to approximate the MPI statistic by a marginal density obtained from a mixture of conditional Inverted Beta (IB) densities with a weight function given by an inverted chi-square density. Critical values and powers are supplied. We apply the IB approximation to test the unit root hypothesis to simulated data, to the Nelson and Plosser data set, to the extended Nelson and Plosser data set and to test the Purchase Power Parity in the real Euro/Dollar exchange rate. |
Keywords and phrases: Bayesian, inverted beta, mixture, small-sample, unit root MPI test. |
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