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Testing for Serial Correlation and Unit Roots Using a Computer Function Routine Bases on ERA's


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This paper initiates a research program to provide computer function routines that can be used to deliver critical values or significance levels for statistical tests. These routines are easily integrated into existing econometric software and can be made available on a user call basis. The mathematical formulae underlying these approximants belong to the family of extended rational approximants (ERA's) introduced in '15. The first part of this paper extends the algebraic theory of ERA's to distribution function approximation. Composite functional approximants are also developed to treat the parameter multidimensionally that is common in practical application. The second part of the paper reports a detailed application of the approach to the distribution of the serial correlation coefficient under spherical Gaussian errors. The formulae we extract are error-corrected Edgeworth approximants that yield at least three decimal place accuracy over the entire distribution for all sample sizes (T >= 4). These approximants can be used to mount a variety of tests, including tests for serial correlation and unit roots. Further extension of this work to higher order serial correlation coefficients that are used in the Box-Jenkins model identification process are discussed in the conclusion.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 721.

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Date of creation: Sep 1984
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Publication status: Published in Advances in Statistical Analysis and Statistical Computing, Vol. 1, JAI Press, 1985, pp. 1-50
Handle: RePEc:cwl:cwldpp:721

Note: CFP 642.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Rational approximation; serial correlation; computer function routines; critical values;


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  1. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
  2. Peter C.B. Phillips, 1983. "Finite Sample Econometrics Using ERA's," Cowles Foundation Discussion Papers 683, Cowles Foundation for Research in Economics, Yale University.
  3. Peter C.B. Phillips, 1982. "ERA's: A New Approach to Small Sample Theory," Cowles Foundation Discussion Papers 645, Cowles Foundation for Research in Economics, Yale University.
  4. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-85, March.
  5. Peter C.B. Phillips, 1981. "Marginal Densities of Instrumental Variable Estimators in the General Single Equation Case," Cowles Foundation Discussion Papers 609, Cowles Foundation for Research in Economics, Yale University.
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