ON THE STATIONARY PROBABILITY DENSITY FUNCTION OF BILINEAR TIME SERIES MODELS: A NUMERICAL APPROACH

Abstract
In this paper, we show that the Chapman-Kolmogorov formula could be used as
a recursive formula for computing the m-step-ahead conditional density of a Markov
bilinear model. The stationary marginal probability density function of the model
may be approximated by the m-step-ahead conditional density for sufficiently large
m.