A flexible univariate moving average time-series model for dispersed count data

Journal of Statistical Distributions and Applications

Table 1 Estimated mean, variance, and autocorrelation for various SCMPMA(1) data simulations of length 10,000 given parameters, (λ,ν,m₁,m₂); λ=0.5 for all simulations

m₁	m₂	ν	Est. Mean	True Mean	Est. Var.	True Var.	\(\hat {\rho }\)	ρ
1	1	0	3.0073	3.00	5.9076	6.00	0.333	0.333
		0.5	1.8846		2.3395		0.335	0.333
		1	1.4842	1.50	1.4507	1.50	0.328	0.333
		2	1.2359		1.0358		0.338	0.333
		35	0.9826	1.00	0.6568	0.67	0.333	0.333
1	2	0	4.0027	4.00	8.0309	8.00	0.248	0.250
		0.5	2.4891		3.0010		0.253	0.250
		1	1.9861	2.00	1.9755	2.00	0.252	0.250
		2	1.6427		1.3284		0.257	0.250
		35	1.3355	1.33	0.8964	0.89	0.254	0.250
2	1	0	5.0408	5.00	10.2256	10.00	0.404	0.400
		0.5	3.1414		3.9010		0.402	0.400
		1	2.4823	2.50	2.4689	2.50	0.396	0.400
		2	2.0094		1.6561		0.401	0.400
		35	1.6583	1.67	1.1135	1.11	0.390	0.400
2	2	0	6.0019	6.00	12.2343	12.00	0.331	0.333
		0.5	3.7195		4.5267		0.338	0.333
		1	2.9873	3.00	3.0130	3.00	0.329	0.333
		2	2.4488		2.0178		0.336	0.333
		35	1.9861	2.00	1.2964	1.33	0.326	0.333

For the special cases (i.e. ν=0,1,35, where ν=35 sufficiently represents performance as ν→∞), we likewise provide the expected/true mean and variance. Along with the estimated autocorrelation \(\hat {\rho }\) that results from the data, the table reports the true autocorrelation, \(\rho _{1} = \frac {m_{1}}{2m_{1}+m_{2}}\), for all {m₁,m₂} and any ν (Eq. (22))