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

Table 3

Summary statistics for the PL estimator for different parameter values , using an exponential kernel (representing short-range dependence) at various sample lengths of the series for a semi-Poisson Lévy-based process.

N	True value
		5	2	4	0.7	9	0.3	15	0.05
200	Mean	4.9292	1.9996	3.9292	0.6996	8.9292	0.2996	14.9292	0.0496
	Bias	0.0151	0.0097	0.0101	0.0032	0.0356	−0.0010	0.0656	−0.0097
	MSE	0.0458	0.0190	0.0205	0.0021	0.2541	0.0002	0.8618	0.0190
N	True value	5	2	4	0.7	9	0.3	15	0.05
500	Mean	4.9552	1.9251	3.9552	0.6999	8.9552	0.2999	14.9552	0.0499
	Bias	0.0061	0.0038	0.0041	0.0012	0.0143	−0.0004	0.0261	−0.0019
	MSE	0.0186	0.0076	0.0084	0.0008	0.1023	0.0000	0.3408	0.0018
N	True value	5	2	4	0.7	9	0.3	15	0.05
1000	Mean	4.9683	1.9999	3.9683	0.6999	8.9983	0.2999	14.9683	0.0499
	Bias	0.0030	0.0019	0.0021	0.0001	0.0071	−0.0002	0.0131	−0.0004
	MSE	0.0094	0.0038	0.0047	0.0000	0.0513	0.0000	0.1734	0.0002