THE ESTIMATION OF CONTINUOUS PARAMETER LONG-MEMORY TIME-SERIES MODELS

A class of univariate fractional ARIMA models with a continuous time p arameter is developed for the purpose of modeling long-memory time ser ies. The spectral density of discretely observed data is derived for b oth point observations (stock variables) and integral observations (fl ow variables). A frequency domain maximum likelihood method is propose d for estimating the long-memory parameter and is shown to be consiste nt and asymptotically normally distributed, and some issues associated with the computation of the spectral density are explored.