Forecasting COVID-19 cases using time series modeling and association rule mining

Somyanonthanakul, Rachasak; Warin, Kritsasith; Amasiri, Watchara; Mairiang, Karicha; Mingmalairak, Chatchai; Panichkitkosolkul, Wararit; Silanun, Krittin; Theeramunkong, Thanaruk; Nitikraipot, Surapon; Suebnukarn, Siriwan

doi:10.1186/s12874-022-01755-x

BMC Medical Research Methodology

Table 2 The results of time series analysis model applied to six training sets obtained from statistical tests: Coefficient of determination (R²), Root mean square error (RMSE), Mean absolute error (MAE)

From: Forecasting COVID-19 cases using time series modeling and association rule mining

No	Model	All Wave			Wave 1			Wave 2			Wave 3			Wave 4			Wave 3–4
No	Model	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE	R2	RMSE	MAE
1	I(1)	0.0899	290.7718	283.8123	0.0331	325.9969	323.9485	0.0904	277.9974	273.4644	0.0328	94.5392	75.6991	0.0145	65.7031	65.7790	0.0522	63.3078	63.8452
2	I(2)	0.2199	188.6716	178.0013	0.2199	325.9572	323.9855	0.2972	285.9000	280.6391	0.0425	77.1222	68.0936	0.0048	83.1201	73.3845	0.0425	80.7247	71.4506
3	AR(1)	0.5835	52.9774	44.8681	0.5172	334.5952	332.3318	0.5186	318.9675	315.8692	0.2275	85.0022	67.6283	0.5543	60.0630	49.5482	0.4259	30.1341	25.6407
4	AR(2)	0.5326	48.9132	45.3217	0.5543	338.2526	336.1396	0.0169	298.2876	295.3547	0.0001	78.0756	66.2715	0.3493	35.2782	26.6954	0.1111	57.0969	46.8206
5	AR(3)	0.5026	71.3773	67.2935	0.5969	337.3307	335.1067	0.1671	292.9912	290.9822	0.0084	82.1250	69.8914	0.1274	53.4205	42.5510	0.1001	61.1195	51.1240
6	MA(1)	0.0004	176.9638	171.7192	0.0004	327.4278	325.3349	0.0004	294.4148	292.0716	0.0004	81.4992	72.4591	0.0004	81.6120	71.7955	0.0004	270.0047	265.8700
7	MA(2)	0.0003	205.0899	199.6313	0.0003	329.3588	327.2778	0.0004	328.9829	326.8977	0.0003	93.4902	85.6784	0.0003	148.8627	141.7412	0.0003	92.1310	83.2050
8	MA(3)	0.0001	307.5673	298.8213	0.0002	328.1374	326.0477	0.0000	333.1808	331.1216	0.0004	149.7222	145.0442	0.0001	125.3216	117.2491	0.0000	79.3442	68.9794
9	ARMA(1,1)	0.5741	40.8981	36.6221	0.5020	334.0945	331.8095	0.4767	315.0413	311.7129	0.1788	85.6014	69.1618	0.5161	42.8637	38.1547	0.3543	33.6863	26.0659
10	ARMA(2,2)	0.5062	67.3449	63.3953	0.6258	339.1666	337.0229	0.0006	299.0722	296.2244	0.5596	203.8326	202.3505	0.1104	56.4891	45.8304	0.0368	72.2012	61.3681
11	ARMA(3,3)	0.5089	68.0282	64.0255	0.6393	334.7573	332.3653	0.0009	306.0231	303.3267	0.1338	147.5160	142.7802	0.1028	56.5914	45.7511	0.3217	62.0183	56.2090
12	ARIMA(1,1,1)	0.4182	121.1567	105.5253	0.0007	327.7731	325.6391	0.3813	275.0749	269.6568	0.2256	61.1524	51.7814	0.5694	43.9619	38.7228	0.7279	35.4740	29.4524
13	ARIMA(2,1,2)	0.4496	188.1384	175.6110	0.1136	331.8481	329.6721	0.0337	274.7054	269.5087	0.5424	241.8948	239.8888	0.0361	60.5829	48.7030	0.8066	37.8168	33.3437
14	ARIMA(3,1,3)	0.5746	100.8429	93.3260	0.0072	327.6217	325.5377	0.1379	291.6125	282.3766	0.0935	145.4436	140.7227	0.0324	60.5233	48.3732	0.2291	99.0573	92.0246
15	ARIMA(1,2,1)	0.6227	22.8141	19.4113	0.0022	327.9731	325.8776	0.5564	307.1235	303.0277	0.1896	85.9017	69.5801	0.5616	43.7555	38.6440	0.3546	33.6537	26.0567
16	ARIMA(2,2,2)	0.5811	108.9374	99.9407	0.0042	330.6365	328.5217	0.0735	280.7723	274.8963	0.5010	221.8999	220.2538	^a0.5853	^a29.7605	^a27.6102	0.0367	78.2477	67.6000
17	ARIMA(3,2,3)	0.5684	105.7827	98.0635	0.0399	328.8342	326.6476	0.0782	269.6121	246.3643	0.7882	147.4570	143.0789	0.1616	85.7303	66.8601	0.3501	81.0317	75.6607
18	I(1) + X1	0.0037	288.6017	283.7774	0.0490	326.2426	324.0655	0.0342	282.0157	279.3011	0.0000	99.6746	75.6989	0.0000	81.8578	72.0013	0.0044	103.9072	83.0929
19	I(2) + X1	0.2592	212.5173	197.9378	0.2592	326.2460	324.1258	0.0005	286.8855	283.5395	0.0019	99.7003	76.0409	0.0048	83.1201	73.3845	0.0068	103.7216	83.5353
20	AR(1) + X1	0.6067	610.2414	519.6976	0.1226	326.8148	324.8728	0.2344	232.7690	219.5232	0.4300	38.4820	32.1837	0.6319	249.6770	198.6695	0.0122	268.9514	263.4326
21	AR(2) + X1	0.5362	67.2016	59.9040	0.1071	327.5698	325.6145	0.0035	263.3728	258.8025	0.6491	36.7028	29.6225	0.3990	88.3833	67.2515	0.8336	100.1792	83.2140
22	AR(3) + X1	0.6796	75.6844	55.5952	0.0890	326.4052	324.4467	0.0017	271.8932	267.0636	0.6816	37.0752	29.5750	0.0373	59.1096	47.5392	0.8428	97.1527	78.2065
23	MA(1) + X1	0.0001	252.3404	248.6892	0.1281	336.3468	334.3429	0.0013	298.9810	296.1156	0.0084	104.0982	76.0860	0.0313	87.0295	76.0244	0.0176	103.1149	81.7565
24	MA(2) + X1	0.0702	221.6587	216.9112	0.2267	335.3732	333.4037	0.1160	336.7430	334.5787	0.0004	75.8666	55.0494	0.0382	134.9549	127.8984	0.0138	88.1465	75.0825
25	MA(3) + X1	0.0005	317.8255	309.4642	0.1913	329.5174	327.5438	0.0001	334.6743	332.6033	0.0060	113.7286	77.5648	0.0139	118.1786	109.4121	0.0008	87.2773	72.8789
26	ARMA(1,1) + X1	0.5916	413.4365	358.2175	0.1774	324.0025	322.1328	0.1541	251.9922	243.5882	0.4516	33.2501	26.5740	0.6405	220.4147	176.9939	0.6106	165.2220	163.3853
27	ARMA(2,2) + X1	0.5949	424.4358	366.5745	0.0723	331.6259	329.4747	0.3369	399.6066	398.4546	0.7118	171.6618	170.5084	0.4607	160.5215	149.9203	0.4951	88.6736	83.4224
28	ARMA(3,3) + X1	0.1833	113.5424	100.8362	0.2160	327.6383	325.7101	0.0107	339.7625	337.6229	0.5940	167.3714	164.8800	0.5863	107.5209	84.9299	0.0044	219.6314	192.1180
29	ARIMAX(1,1,1) + X1	0.4182	183.8188	166.3895	0.1277	322.2422	320.3213	0.2574	267.9366	262.3262	0.5140	45.4581	37.5053	0.5694	43.9619	38.7228	0.7704	83.1827	79.9974
30	ARIMAX(2,1,2) + X1	0.6784	124.4039	99.0967	0.2633	321.7203	319.9461	0.0425	285.4226	281.3559	0.6366	176.3529	174.5772	0.0361	60.5829	48.7030	0.8382	59.1795	47.6580
31	ARIMAX(3,1,3) + X1	0.6510	149.8496	127.6797	0.0302	336.0062	333.9879	0.0007	253.1438	247.7629	0.1191	144.5963	139.6924	0.0324	60.5233	48.3732	0.3812	55.4460	50.4435
32	ARIMAX(1,2,1) + X1	0.2403	143.0063	130.9023	0.1210	322.0322	320.1035	0.2928	278.2316	273.1433	0.4498	49.7481	41.2963	0.5616	43.7555	38.6440	0.7471	79.9917	76.4410
33	ARIMAX(2,2,2) + X1	0.2168	95.7906	88.9073	0.3083	316.7929	315.1248	0.0490	287.2771	283.2256	0.5580	207.7418	206.2698	0.5853	29.7605	27.6102	0.1473	98.7315	80.6377
34	ARIMAX(3,2,3) + X1	0.4787	63.5331	57.3825	0.1452	337.2546	335.2641	0.0016	257.9516	251.6657	0.0026	144.7672	139.9775	0.1616	85.7303	66.8601	0.4676	74.2653	70.1748
35	I(1) + X2	0.0447	289.1389	281.2524	0.0041	326.0347	323.9383	0.0884	278.0144	273.4693	0.0000	99.6750	75.6992	0.0000	81.8175	71.9843	0.0044	103.9073	83.0939
36	I(2) + X2	0.0105	249.4103	231.4904	0.0421	326.0106	323.9672	0.2082	284.7981	279.4427	0.0019	99.6955	76.0373	0.0048	83.2961	73.5082	0.0068	104.7077	83.9761
37	AR(1) + X2	0.6156	255.7645	212.8672	0.5172	334.5952	332.3319	0.1727	302.2914	298.4389	0.0282	69.9752	58.5275	0.6311	249.1627	198.4651	0.5834	41.9315	35.5895
38	AR(2) + X2	0.5858	64.0891	52.3809	0.5543	338.2531	336.1401	0.0007	293.3307	290.4134	0.0131	70.7792	58.5222	0.3373	82.2578	62.6506	0.4830	42.5877	37.2450
39	AR(3) + X2	0.5264	28.4479	22.4192	0.5969	337.3308	335.1069	0.1030	298.6989	296.3389	0.0111	72.7548	60.1599	0.0092	57.7292	46.8582	0.4188	51.2708	45.6610
40	MA(1) + X2	0.0004	191.3896	187.3443	0.0004	327.4278	325.3349	0.0064	303.3572	300.9790	0.0116	81.3063	71.5271	0.0307	98.0537	87.9097	0.1876	275.7095	268.5105
41	MA(2) + X2	0.0003	208.8616	204.3860	0.0003	329.3588	327.2778	0.0071	329.9775	327.9153	0.0164	94.5079	86.0634	0.0638	143.4629	136.7615	0.0215	93.9181	84.8925
42	MA(3) + X2	0.0000	313.7185	303.9636	0.0002	328.3339	326.2458	0.0050	333.2174	331.1693	0.0168	83.1832	74.0123	0.0624	136.5470	125.2288	0.0435	87.0651	77.3405
43	ARMA(1,1) + X2	0.6070	188.6286	158.6611	0.5020	334.0945	331.8095	0.2345	301.7636	297.9054	0.0152	80.3589	66.8892	0.6260	208.8213	169.3105	0.6516	76.7976	69.1291
44	ARMA(2,2) + X2	0.5069	71.3063	67.2141	0.6257	339.1664	337.0227	0.0149	301.8609	298.7972	0.5278	160.9546	157.4370	0.4919	188.1245	174.4431	0.3916	113.9236	106.8338
45	ARMA(3,3) + X2	0.5675	30.4833	28.1090	0.1795	324.3882	322.5190	0.3004	308.7024	303.8821	0.5828	157.7017	154.2446	0.6386	253.0751	196.3018	0.1300	43.9619	38.7226
46	ARIMAX(1,1,1) + X2	0.3531	168.2529	153.0882	0.0929	318.2668	316.3056	0.2369	268.3102	262.7485	0.4671	50.0191	41.8890	^a0.5695	^a27.7508	^a23.4642	0.7704	83.1909	80.0059
47	ARIMAX(2,1,2) + X2	0.6484	174.1887	148.7599	0.2435	324.9496	322.5022	0.0147	269.1468	263.4866	0.6058	198.4915	197.1301	0.0519	59.5415	47.9796	0.8380	60.6156	48.6302
48	ARIMAX(3,1,3) + X2	0.6375	170.1995	146.9692	0.1756	323.9133	322.0434	0.0324	275.3298	266.7312	0.0229	144.4264	139.5740	0.0474	59.5452	47.7400	0.0752	91.5523	75.5956
49	ARIMAX(1,2,1) + X2	0.0823	124.5007	114.6162	0.1758	324.0920	322.2535	0.2380	277.5598	272.5563	0.4500	49.7456	41.2962	0.5460	43.4074	38.4491	0.7471	80.0006	76.4500
50	ARIMAX(2,2,2) + X2	0.6342	40.4552	34.6242	0.0904	277.9974	273.4644	0.0191	270.5990	264.7709	0.5524	217.1144	215.5897	0.0927	85.8890	67.4658	0.8189	72.6105	57.7871
51	ARIMAX(3,2,3) + X2	0.6638	33.3190	25.3416	0.2972	285.9000	280.6391	0.0443	266.4733	258.2639	0.7216	146.7202	142.1839	0.1618	85.7246	66.8524	0.0204	129.1237	118.5442

^a the best time series analysis model performance

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