The p values of structural break tests, when the break date
or dates are unknown, must be calculated in terms of the probability
distributions of functions of Bessel processes. The literature so far
has maintained that direct computation of these p values and
of the corresponding critical values is too difficult and has relied on
approximations based on simulations, asymptotic expansions, or curve
fitting. This paper presents a fast simple method of calculating exact
p values and critical values and uses the method to evaluate
the accuracy of the various approximations.The
author is grateful for comments and suggestions from Don Andrews, Clint
Cummins, Jeff Fuhrer, Ken Garbade, Jim Mahoney, Tony Rodrigues, Josh
Rosenberg, Sebastian Schich, participants in a workshop at the Federal
Reserve Bank of New York, and the referees. The views expressed in this
paper are those of the author and do not necessarily represent those of the
Federal Reserve Bank of New York or the Federal Reserve System.