The Estimation of Continuous Parameter Long-Memory Time Series Models
针对长记忆时间序列，提出了一类连续时间参数的分数ARIMA模型，推导了离散观测数据的谱密度，并给出频域极大似然估计方法，证明其一致性和渐近正态性。
A class of univariate fractional ARIMA models with a continuous time parameter is developed for the purpose of modeling long-memory time series. The spectral density of discretely observed data is derived for both point observations (stock variables) and integral observations (flow variables). A frequency domain maximum likelihood method is proposed for estimating the longmemory parameter and is shown to be consistent and asymptotically normally distributed, and some issues associated with the computation of the spectral density are explored.