Univariate Conditional Distributions of an Open-Loop TAR Stochastic Process

Clusters of large values are observed in sample paths of certain open-loop threshold autoregressive (TAR) stochastic processes. In order to characterize the stochastic mechanism that generates this empirical stylized fact, three types of marginal conditional distributions of the underlying stochastic process are analyzed in this paper. One allows us to find the conditional variance function that explains the aforementioned stylized fact. As a by-product, we are able to derive a sufficient condition to have asymptotic weak stationarity in an open-loop TAR stochastic process.