The program apvals.f (for Unix; a version in DOS format is apvals.for)
computes approximate asymptotic P values for unit root and cointegration
tests using approximations given in the paper:

  James G. MacKinnon, ``Approximate asymptotic distribution functions
  for unit root and cointegration tests,'' JBES, 12, April 1994.

P values are provided for both tau tests and z tests, for up to 6
possibly cointegrated variables.

The main program is supplied primarily as an example.  The actual
calculations are done in the subroutines pvtau and pvz, which should
generally be incorporated directly into user code.  Both these routines
call the routine ddnor to compute the cumulative normal distribution.

A compiled version of apvals.f, apvals.exe, should run on any
Intel-based PC with a math coprocessor.  It is provided for the
convenience of those who do not have access to a Fortran compiler.
This exe file must be transferred in binary mode.

A better approach to the same problem has been taken in the paper

  James G. MacKinnon, "Numerical distribution functions for unit root and
  cointegration tests," Journal of Applied Econometrics, 11, 1996,
  601-618.

The programs for this paper, and the tables of results that they use, are
available from my home page.

Legal disclaimer follows:

  These programs are provided on an "as is" basis.  There is no
  warranty, express or implied.  They have been tested and appear
  to work correctly when given sensible input values, using the Lahey
  F77L-EM/32 compiler.


James G. MacKinnon                       Department of Economics
    phone: 613 533-2293                  Queen's University
      Fax: 613 533-6668                  Kingston, Ontario, Canada
    Email: jgm@qed.econ.queensu.ca       K7L 3N6
Home Page: http://www.econ.queensu.ca/pub/faculty/mackinnon/

July 14, 1993
Revised, November 13, 1997