The marginal distribution function of threshold-type processes with central symmetric innovations

This paper addresses the problem of finding exact and explicit (closed-form) expressions for the stationary marginal distribution of threshold-type time series processes, their associated moments, autocovariance and autocorrelation coefficients. The innovation process of the models under consideration follows three central symmetric distribution functions: Gaussian, Laplace, and Cauchy. Theoretical results for both two- and three-regime threshold-type models are derived. Various examples give rise to a deeper understanding of certain features of the stationary process structure. Exact results for the stationary density, central moments, and autocorrelations of threshold-type processes are compared with approximate density and moment results obtained through an existing numerical methods.

Automated summary

This paper addresses the problem of finding exact and explicit expressions for the stationary marginal distribution of threshold-type time series processes, and their associated moments, autocovariance and autocorrelation coefficients. Theoretical results for two- and three-regime threshold-type models are derived and various examples provide a deeper understanding of certain features of the stationary process structure. Exact results are compared with approximate results obtained through an existing numerical method for the stationary density, central moments, and autocorrelations of threshold-type processes.