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 . 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.
Phillips, Peter C.B. and Reiss, Peter C., "Testing for Serial Correlation and Unit Roots Using a Computer Function Routine Based on ERA's" (1984). Cowles Foundation Discussion Papers. 960.