  In this paper, we consider a continuous-time autoregressive fractionally
integrated moving average (CARFIMA) model, which is defined as the stationary
solution of a stochastic differential equation driven by a standard fractional
Brownian motion. Like the discrete-time ARFIMA model, the CARFIMA model is
useful for studying time series with short memory, long memory and
antipersistence. We investigate the stationarity of the model and derive its
covariance structure. In addition, we derive the spectral density function of a
stationary CARFIMA process.
