Critical Values and P Values of Bessel Process Distributions: Computation and Application to Structural Break Tests

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.