This paper shows that a large dimensional vector autoregressive model (VAR) of finite order can generate fractional integration in the marginalized univariate series. We derive high-level assumptions under which the final equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two specific models.
CHEVILLON, G., HECQ, A. et LAURENT, G. (2018). Generating Univariate Fractional Integration within a Large VAR(1), Journal of Econometrics, 1(204), pp. 54-65.