A Class of Generalized Long-Memory Time Series Models
A. E. Brockwell
This paper introduces a family of ``generalized long-memory time
series models'', in which observations have a specified conditional
distribution, given a latent Gaussian
fractionally integrated autoregressive moving average (ARFIMA) process.
The observations may have discrete or continuous distributions
(or a mixture of both).
The family includes existing models such as ARFIMA models themselves,
long-memory stochastic volatility models, long-memory censored
Gaussian models, and others. Although the family of models
is flexible, the latent long-memory process poses
problems for analysis. Therefore we introduce a
Markov chain Monte Carlo sampling algorithm and develop a
set of recursions which make it feasible.
This makes it possible, among other things,
to carry out exact likelihood-based
analysis of a wide range of non-Gaussian long-memory models
without resorting to the use of likelihood approximations.
also yields predictive distributions that take into
account model parameter uncertainty.
The approach is demonstrated in two case studies.