Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails

Table 4

Summary statistics for the PL estimator for different parameter values and different sample lengths of the series with long-range dependence semi-Poisson Lévy-based process.

N	True value
		2	0.8	0.2	3	1.6	0.6	1.3	3	0.3
100	Mean	1.8161	0.8414	0.1329	3.1862	1.2904	0.6178	1.3012	2.8738	0.2210
	Bias	0.1838	−0.0414	0.0671	−0.1862	0.3096	−0.0178	−0.0012	0.1261	0.3
	MSE	0.0654	0.0209	0.0574	0.0346	0.0958	0.0003	0.0280	0.0359	0.09
250	Mean	1.9398	0.8203	0.2081	3.0856	1.2957	0.5884	1.2911	2.973	0.3410
	Bias	0.0601	−0.0203	−0.0081	−0.0855	0.3043	0.0115	−0.0000	0.0269	0.0003
	MSE	0.0077	0.0140	0.0044	0.0283	0.0104	0.0077	0.0000	0.0209	0.0000
500	Mean	2.0032	0.8111	0.2029	3.0065	1.5594	0.6222	1.3001	3.0001	0.3041
	Bias	0.0223	0.0102	0.0011	−0.0064	0.0004	0.0081	0.0000	0.0000	0.0000
	MSE	0.0049	0.0079	0.0021	0.0038	0.0058	0.0031	0.0000	0.0000	0.0000
N	True value	1.5	1	0.6	1	0.4	0.2	3	0.6	0.9
30	Mean	1.6158	0.8636	0.4518	0.9091	0.6454	0.1524	3.3537	0.5939	0.7143
	Bias	−0.1158	0.1363	0.1482	0.0908	−0.2454	0.0475	−0.3536	0.0060	0.1856
	MSE	0.0383	0.0478	0.0541	0.0354	0.0751	0.0448	0.1274	0.0072	0.0561
500	Mean	1.5808	0.8860	0.6172	0.9671	0.3774	0.1899	3.0793	0.6211	0.8059
	Bias	−0.0807	0.1139	−0.0172	0.0328	0.0225	−0.0022	−0.0792	−0.0211	0.0740
	MSE	0.0065	0.0380	0.0241	0.0010	0.0005	0.0000	0.0064	0.0124	0.0160
1000	Mean	1.5025	0.9933	0.6002	0.9953	0.4029	0.2001	3.0431	0.6065	0.9026
	Bias	−0.0025	0.0766	0.0053	−0.0000	0.0000	0.0000	−0.0431	−0.0056	0.0167
	MSE	0.0000	0.0058	0.0000	0.0000	0.0000	0.0000	0.0027	0.0021	0.0042