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

Table 2

Bias and MSE results of 𝛼 for NSINARMA(1,2) model.

CLS
	𝜆 = 0.3			𝜆 = 5
Sample size	100	300	800	100	300	800
(𝜃1,𝜃2) = (0.1, 0.1)
Bias(α)	−9.8012𝑒−04	−8.0314𝑒−05	−1.2149𝑒−05	1.6030𝑒−05	−2.6319𝑒−05	−7.9892𝑒−06
MSE(α)	2.8819𝑒−04	1.9351𝑒−06	4.4280𝑒−08	7.7085𝑒−07	2.0781𝑒−07	1.9148𝑒−08
(𝜃1,𝜃2) = (0.1, 0.6)
Bias(α)	−9.0876𝑒−04	−1.4515𝑒−04	3.6936𝑒−06	−4.5047𝑒−05	−3.6633𝑒−05	−1.7588𝑒−06
MSE(α)	2.4775𝑒−04	6.3203𝑒−06	4.0928𝑒−09	6.0877𝑒−07	4.0259𝑒−07	9.2803𝑒−10
(𝜃1,𝜃2) = (0.2, 0.3)
Bias(α)	−5.8582𝑒−04	−8.2571𝑒−05	−1.1720𝑒−05	4.7792𝑒−05	−2.2042𝑒−05	−7.8901𝑒−06
MSE(α)	1.0296𝑒−04	2.0454𝑒−06	4.1208𝑒−08	6.8522𝑒−07	1.4575𝑒−07	1.8676𝑒−08
(𝜃1,𝜃2) = (0.3, 0.4)
Bias(α)	−1.0548𝑒−03	−1.3550𝑒−04	−2.1872𝑒−06	−6.0986𝑒−05	−2.1873𝑒−05	−1.6658𝑒−08
MSE(α)	3.3379𝑒−04	5.5082𝑒−06	1.4352𝑒−09	1.1158𝑒−06	1.4353𝑒−07	8.3243𝑒−14
(𝜃1,𝜃2) = (0.4, 0.4)
Bias(α)	−8.9921𝑒−04	−1.4099𝑒−04	−8.5553𝑒−07	−6.6568𝑒−05	−2.2816𝑒−05	1.0669𝑒−07
MSE(α)	2.4257𝑒−04	5.9633𝑒−06	2.1958𝑒−10	1.3294𝑒−06	1.5617𝑒−07	3.4148𝑒−12