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

Table 2

Summary statistics for the MM estimator for different parameter values with different for a Poisson-inverse Gaussian Lévy-based process with long-range dependence.

N	True value
		5	2	4	0.7	7	0.3	1.9	0.05
100	Mean	4.9962	1.9962	3.9962	0.6999	7.0003	0.3004	1.9004	0.0500
	Bias	0.0099	0.0196	−0.0200	0.0019	0.0300	0.0027	−0.0409	−0.0044
	MSE	0.0099	0.0386	0.0401	0.0003	0.0900	0.0007	0.1680	0.0020
N	True value	5	2	4	0.7	7	0.3	1.9	0.05
500	Mean	5.0002	2.0002	4.0002	0.7000	7.0004	0.3004	1.9004	0.0500
	Bias	0.0020	0.0039	−0.0039	0.0004	0.0060	0.0005	−0.0081	−0.0008
	MSE	0.0020	0.0077	0.0079	0.0000	0.0180	0.0001	0.0336	0.0004
N	True value	5	2	4	0.7	7	0.3	1.9	0.05
1000	Mean	4.9997	1.9997	3.9997	0.6999	7.0003	0.3003	1.9003	0.0500
	Bias	0.0009	0.0019	−0.0020	0.0001	0.0030	0.0002	−0.0040	−0.0004
	MSE	0.0009	0.0038	0.0040	0.0000	0.0090	0.0000	0.0168	0.0002