Despite a recent proliferation of research using cyclical long memory, surprisingly little is known regarding the asymptotic properties of likelihood-based methods. Estimators have been studied in both the time and frequency domains for the Gegenbauer autoregressive moving average process...

We review the multiple frequency Gegenbauer autoregressive moving average model, which is able to reproduce a wide range of autocorrelation functions. Extending the result of Chung (1996a), we propose the asymptotic distributions for a conditional sum of squares estimator of the model...