Nonstationary INAR(1) Process with 𝑞th-Order Autocorrelation Innovation

Table 3

Bias and MSE results of 𝛼 for NSINARMA(1,3) model.

CLS
	𝜆 = 0.3			𝜆 = 5
Sample size	100	300	800	100	300	800
(𝜃1,𝜃2,𝜃3) = (0.1, 0.1, 0.1)
Bias(α)	−1.3742𝑒−03	−1.4097𝑒−04	−3.3819𝑒−05	−4.4965𝑒−05	4.5510𝑒−06	−5.1844𝑒−06
MSE(α)	5.6651𝑒−04	5.9616𝑒−06	3.4312𝑒−07	6.0655𝑒−07	6.2135𝑒−08	8.0635𝑒−09
(𝜃1,𝜃2,𝜃3) = (0.1, 0.2, 0.4)
Bias(α)	−2.0218𝑒−03	−9.3641𝑒−05	8.2901𝑒−06	−1.4846𝑒−04	−8.0926𝑒−06	−8.4087𝑒−07
MSE(α)	1.2263𝑒−03	2.6306𝑒−06	2.0618𝑒−08	6.6121𝑒−06	1.9647𝑒−08	2.1212𝑒−10
(𝜃1,𝜃2,𝜃3) = (0.2, 0.1, 0.2)
Bias(α)	−1.0825𝑒−03	−1.1218𝑒−04	−3.0775𝑒−05	−2.0846𝑒−05	7.8758𝑒−06	−4.3565𝑒−06
MSE(α)	3.5154𝑒−04	3.7751𝑒−06	2.8413𝑒−07	1.3037𝑒−07	1.8608𝑒−08	5.6936𝑒−09
(𝜃1,𝜃2,𝜃3) = (0.3, 0.3, 0.3)
Bias(α)	−1.6766𝑒−03	−1.3506𝑒−04	8.8713𝑒−06	−1.3902𝑒−04	−2.6374𝑒−06	−2.3441𝑒−07
MSE(α)	8.4330𝑒−04	5.4723𝑒−06	2.3610𝑒−08	5.7980𝑒−06	2.0868𝑒−09	1.6485𝑒−11
(𝜃1,𝜃2,𝜃3) = (0.5, 0.3, 0.1)
Bias(α)	−1.5676𝑒−03	−1.3084𝑒−04	7.6103𝑒−06	−1.5146𝑒−04	−2.5173𝑒−06	−2.9431𝑒−07
MSE(α)	7.3722𝑒−04	5.1355𝑒−06	1.7375𝑒−08	6.8819𝑒−06	1.9010𝑒−09	2.5985𝑒−11