On continuous-time autoregressive fractionally integrated moving average processes

摘要

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 anti persistence. We investigate the stationarity of the model and derive its covariance structure. In addition, we derive the spectral density function of it stationary CARFIMA process.