The Optimal Bandwidth Parameter Selection in GPH Estimation

Table 1

The optimal bandwidth parameter range under different sequence lengths.

	Existence	Persistence or antipersistence	Estimation accuracy
N = 100	[0.59, 0.68]	[0.58, 0.67]	[0.58, 0.67]
N = 200	[0.58, 0.67]	[0.56, 0.65]	[0.59, 0.68]
N = 300	[0.59, 0.68]	[0.55, 0.64]	[0.60, 0.69]
N = 400	[0.58, 0.67]	[0.53, 0.62]	[0.59, 0.68]
N = 500	[0.57, 0.66]	[0.53, 0.62]	[0.59, 0.68]
N = 600	[0.56, 0.65]	[0.53, 0.62]	[0.59, 0.68]
N = 700	[0.55, 0.64]	[0.53, 0.62]	[0.59, 0.68]
N = 800	[0.55, 0.64]	[0.53, 0.62]	[0.58, 0.67]
N = 900	[0.56, 0.65]	[0.52, 0.61]	[0.59, 0.68]
N = 1000	[0.54, 0.63]	[0.52, 0.61]	[0.59, 0.68]
N = 2000	[0.53, 0.62]	[0.52, 0.61]	[0.60, 0.69]
N = 5000	[0.53, 0.62]	[0.55, 0.64]	[0.60, 0.69]
N = 10000	[0.53, 0.62]	[0.55, 0.64]	[0.59, 0.68]
N = 50000	[0.54, 0.63]	[0.59, 0.68]	[0.60, 0.69]
Intersection	[0.59, 0.62]	[0.58, 0.61]	[0.60, 0.67]

Note: the optimal parameter range bandwidth in the table should be discrete points, but in order to save space, it is expressed as an interval number.