Abstract
<p>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.</p>
Highlights
In the context of nonlinear stochastic processes, Tong (1990) proposed the open-loop threshold autoregressive (TAR) process and, among many others, Nieto (2005, 2008) and Nieto, Zhang & Li (2013) developed a Bayesian methodology to analyze particular cases, namely-when the threshold variable is not a covariable
The main goal of this paper is to obtain univariate marginal conditional distributions for the open-loop TAR process in order to explain the presence of large-sample clusters in a sample path
As a by-product, we provide a sufficient condition to have asymptotic weak stationarity of the TAR process which is considered in this paper
Summary
In the context of nonlinear stochastic processes, Tong (1990) proposed the open-loop threshold autoregressive (TAR) process and, among many others, Nieto (2005, 2008) and Nieto, Zhang & Li (2013) developed a Bayesian methodology to analyze particular cases, namely-when the threshold variable is not a covariable. Sample paths in this kind of TAR process can exhibit clusters of (either positive or negative) large values, which is an empirical fact that is observed, for example, in financial and meteorological/hydrological time series.
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