Algorithm AS 153: Pan's Procedure for the Tail Probabilities of the Durbin-Watson Statistic

DESCRIPTION AND PURPOSE A problem that arises naturally in the context of the Durbin-Watson test for serial correlation (1950, p. 413) is the evaluation of the probability that Al U +22 U2 + Ai+ m U2 2 >... > Am are fixed numbers and U1, U2, ..., um are independent standard normal variates. This problem may be solved by Imhof s procedure (1961) which has been programmed in Fortran by Koerts and Abrahamse (1969, pp. 159-160). But recently Durbin and Watson (1971) have drawn attention to an alternative due to Pan (1964) and the algorithm described here is a modification of their variant of Pan's procedure. Pan's original algorithm is available in Fortran as part of White's (1978) SHAZAM program. Our algorithm evaluates