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In this paper, we consider a continuous-time autoregressive fractionallyintegrated moving average (CARFIMA) model, which is defined as the stationarysolution of a stochastic differential equation driven by a standard fractionalBrownian motion. Like the discrete-time ARFIMA model, the CARFIMA model isuseful for studying time series with short memory, long memory andantipersistence. We investigate the stationarity of the model and derive itscovariance structure. In addition, we derive the spectral density function of astationary CARFIMA process.

On continuous-time autoregressive fractionally integrated moving average processes