COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 721 "Testing for Serial Correlation and Unit Roots Peter C.B. Phillips and Peter C. Reiss September 1984 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. |
