Abstract
The first passage time problem for an autoregressive process AR(p) is
examined. When the innovations are gaussian, the determination of the first pas-
sage time probability distribution is closely related to computing a multidimensional
integral of a suitable gaussian random vector, known in the literature as orthant prob-
ability. Recursive equations involving the first passage time probability distribution
are given and a numerical scheme is proposed which takes advantage of the recursion.
Compared with the existing procedures in the literature, the algorithm we propose
is computationally less expensive and reaches a very good accuracy. The accuracy is
tested on some closed form expressions we achieve for special choices of the AR(p)
parameters.
