We discuss computational aspects of likelihood-based estimation of univariate ARFIMA(p, d, q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.

The elevation of Great Salt Lake (GSL) has a great impact on the people of Utah. The flood of GSL in 1982 has caused a loss of millions of dollars. Therefore, it is very important to predict the GSL levels as precisely as possible. This paper points out the reason why conventional methods failed to describe adequately the rise and fall of the GSL levels – the long-range dependence (LRD) propert...

This paper extends the results of Byers, Davidson and Peel (1997) on long memory in support for the Conservative and Labour Parties in the UK using longer samples and additional poll series. It finds continuing support for the ARFIMA(0,d,0) model though with somewhat smaller values of the long memory parameter. We find that the move to telephone polling in the mid-1990s has no apparent effect o...

Gegenbauer processes allow for flexible and convenient modeling of time series data with multiple spectral peaks, where the qualitative description of these peaks is via the concept of cyclical long-range dependence. The Gegenbauer class is extensive, including ARFIMA, seasonal ARFIMA, and GARMA processes as special cases. Model estimation is challenging for Gegenbauer processes when multiple z...