Abstract
A new class of models, generalized exponential model (GEXP), is proposed for modeling seasonal long-memory processes which is a combination of a Gegenbauer model and a Bloomfield model. For inference, two estimation procedures are proposed in the frequency-domain; one is the traditional OLS approach the other is the Lasso approach. Due to different estimation methods, different model determination criteria are used. The performance of the Lasso estimator is investigated and compared with those obtained by the traditional OLS method in finite sample via simulation studies. Based on simulation results, we find that the long-memory estimate by the Lasso approach is less sensitive to bad performance of the estimator for the Gegenbauer frequency. We also find that, for the data with larger sample size, the model selected by the Lasso approach is similar to the OLS approach. But, for most of the cases, the OLS approach provides smaller MISE which measures the difference between the actual and the fitted spectral densities. For illustration, the methodology is applied to the sunspot data.