The estimation of continuous parameter long-memory time series models

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 long-memory parameter and is shown to be consistent and asymptotically normally distributed, and some issues associated with the computation of the spectral density are explored.