The Optimal Bandwidth Parameter Selection in GPH Estimation

Abstract

In this paper, the optimal bandwidth parameter is investigated in the GPH algorithm. Firstly, combining with the stylized facts of financial time series, we generate long memory sequences by using the ARFIMA (1, d, 1) process. Secondly, we use the Monte Carlo method to study the impact of the GPH algorithm on existence test, persistence or antipersistence judgment of long memory, and the estimation accuracy of the long memory parameter. The results show that the accuracy of above three factors in the long memory test reached a relatively high level within the bandwidth parameter interval of 0.5 < a < 0.7. For different lengths of time series, bandwidth parameter a = 0.6 can be used as the optimal choice of the GPH estimation. Furthermore, we give the calculation accuracy of the GPH algorithm on existence, persistence or antipersistence of long memory, and long memory parameter d when a = 0.6.