Empirical Likelihood Testing for Memory Parameter in Gaussian and Non-Gaussion Stationary Time Series

In this paper, we apply empirical likelihood for testing the significance of long memory parameter in Gaussian and non-Gaussian stationary model. We start from the wide-used long memory model (ARFIMA) to derive the empirical likelihood ratio statistics of memory parameter. We show that the testing statistics follow chi-square distribution in theory. The numerical simulations and a real data analysis verify our proposed methods are valid for testing the long memory parameter in stationary ARFIMA models.