Table 1 Parameter estimates and their mean squared errors for INAR\((2)_{S}\) model.

From: Some developments on seasonal INAR processes with application to influenza data

n	\(\hat{\lambda _1}_{ YW}\)	\(\hat{\lambda _2}_{ YW}\)	\(\hat{\mu _{\nu }}_{{ YW}}\)	\(\hat{\lambda _1}_{{ CLS}}\)	\(\hat{\lambda _2}_{{ CLS}}\)	\(\hat{\mu _{\nu }}_{ CLS}\)
\(\lambda _1=0.2\), \(\lambda _2=0.3\), \(\mu _{\nu }=0.9\)
300	0.1608	0.1193	1.1578	0.1986	0.2923	0.9120
300	0.0055	0.0351	0.0788	0.0081	0.0101	0.0225
500	0.1924	0.1997	1.0531	0.1950	0.2935	0.9154
500	0.0025	0.0119	0.0314	0.0031	0.0040	0.0117
1000	0.2035	0.2547	0.9654	0.1989	0.2963	0.9069
1000	0.0015	0.0033	0.0094	0.0014	0.0015	0.0054
1500	0.2026	0.2711	0.9432	0.1985	0.2974	0.9047
1500	0.0009	0.0017	0.0054	0.0009	0.0009	0.0035
\(\lambda _1=0.3\), \(\lambda _2=0.4\), \(\mu _{\nu }=0.75\)
300	0.2152	0.1824	1.0753	0.2900	0.3937	0.7690
300	0.0116	0.0510	0.1295	0.0073	0.0103	0.0259
500	0.2718	0.2556	0.9927	0.2959	0.3885	0.7670
500	0.0038	0.0233	0.0738	0.0032	0.0043	0.0145
1000	0.2978	0.3346	0.8809	0.2969	0.3938	0.7674
1000	0.0014	0.0055	0.0252	0.0014	0.0016	0.0085
1500	0.3022	0.3563	0.8388	0.2994	0.3962	0.7567
1500	0.0009	0.0029	0.0129	0.0009	0.0010	0.0050
\(\lambda _1=0.4\), \(\lambda _2=0.3\), \(\mu _{\nu }=1.333\)
300	0.3944	0.1469	1.7433	0.3933	0.2954	1.3582
300	0.0110	0.0631	0.4273	0.0090	0.0114	0.0574
500	0.3941	0.1455	1.7445	0.3980	0.2938	1.3547
500	0.0027	0.0251	0.1878	0.0036	0.0042	0.0301
1000	0.4165	0.2295	1.5181	0.3990	0.2947	1.3560
1000	0.0017	0.0062	0.0473	0.0014	0.0015	0.0168
1500	0.4163	0.2525	1.4479	0.3990	0.2973	1.3502
1500	0.0012	0.0031	0.0232	0.0010	0.0010	0.0124
\(\lambda _1=0.6\), \(\lambda _2=0.2\), \(\mu _{\nu }=1\)
300	0.4066	0.0557	1.5797	0.5912	0.1984	1.0170
300	0.0439	0.0244	0.4013	0.0084	0.0097	0.0483
500	0.5138	0.1025	1.4430	0.5915	0.1957	1.0293
500	0.0113	0.0119	0.2321	0.0044	0.0043	0.0304
1000	0.5759	0.1510	1.2525	0.5982	0.1965	1.0136
1000	0.0024	0.0036	0.0806	0.0017	0.0018	0.0159
1500	0.5893	0.1679	1.1633	0.5965	0.1985	1.0156
1500	0.0012	0.0019	0.0395	0.0012	0.0011	0.0125

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