  We propose a setup for fractionally cointegrated time series which is
formulated in terms of latent integrated and short-memory components. It
accommodates nonstationary processes with different fractional orders and
cointegration of different strengths and is applicable in high-dimensional
settings. In an application to realized covariance matrices, we find that
orthogonal short- and long-memory components provide a reasonable fit and
competitive out-of-sample performance compared to several competing methods.
