The Optimal Bandwidth Parameter Selection in GPH Estimation

Weijie Zhou,Huihui Tao,Feifei Wang,Weiqiang Pan,Xiangfeng Yang

doi:10.1155/2021/2876000

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.

Highlights

Long-term memory widely exists in the fields of biology, medicine, geology, hydrology, climate, and social science fields [1,2,3]
Robinson establishes the asymptotic normality of the GPH estimator, and the results show that it is suitable for stationary and reversible Gaussian vector sequences [28]
In this paper, based on the ARFIMA (1, d, 1) process and some typical features of financial time series, we use the Monte Carlo method to test the impact of parameter a on the existence of long memory, persistence or antipersistence of long memory, and estimation accuracy of the long memory parameter d, so as to give the optimal bandwidth in the GPH algorithm

Summary

Introduction

Long-term memory widely exists in the fields of biology, medicine, geology, hydrology, climate, and social science fields [1,2,3]. It is generally believed that the British hydrologist Hurst was the first to study the long memory characteristics in a system He used Hurst index (H) to depict the long memory strength of a time series [10]. When H ⟶ 0 (or d ⟶ − 0.5), it indicates that the antipersistent long memory of a time series is strong. In this paper, based on the ARFIMA (1, d, 1) process and some typical features of financial time series, we use the Monte Carlo method to test the impact of parameter a on the existence of long memory, persistence or antipersistence of long memory, and estimation accuracy of the long memory parameter d, so as to give the optimal bandwidth in the GPH algorithm.

The GPH Semiparametric Method of Long Memory Estimation

Simulation Method and Validation Rules

Result

Findings

Conclusions