A new class of parametric estimations for cyclical long memory models, called simulated Hellinger disparity estimator (SHDE), is introduced. The SHDE minimizes the Hellinger distance between the nonparametrically estimated density of the observed data and that of the simulated samples from the model. The method is a distribution-free parametric inference and applicable to the situation where the closed-form expression of the model density is intractable but simulating random variables from the model is possible. The robustness of the SMHD estimator is equivalent to the minimum Hellinger distance estimator. Asymptotic properties of the estimator are established and the performance and the robustness are investigated by simulation study.

long memory, GARMA process, Hellinger disparity, kernel estimator.