Embedding in law of discrete time ARMA processes in continuous time stationary processes

Abstract

© 2018. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Given any stationary time series {Xn : n ¿ Z} satisfying an ARMA(p, q) model for arbitrary p and q with infinitely divisible innovations, we construct a continuous time stationary process {xt : t ¿ R} such that the distribution of {xn : n ¿ Z}, the process sampled at discrete time, coincides with the distribution of {Xn}. In particular the autocovariance function of {xt } interpolates that of {Xn}.Peer ReviewedPostprint (author's final draft