UNISTAT - the ultimate Excel statistics add-in

ARIMA in Excel with Unistat

The Unistat statistics add-in extends Excel with ARIMA capabilities.

Further documentation is available at section 9.1 of the manual, Time Series Analysis > Box-Jenkins ARIMA.

Sample output

Here we provide annotated example report output from the Unistat Excel statistics add-in for data analysis.

ARIMA

Character Plot of Series: Room Averages

X(t) = (1-B) Room Averages

Row	X(t)	-285.0000 182.0000
2	-13.0000	*
3	16.0000	*
4	74.0000	*
5	-33.0000	*
6	87.0000	*
7	96.0000	*
8	-3.0000	*
9	-140.0000	*
10	-43.0000	*
11	-62.0000	*
12	50.0000	*
13	-12.0000	*
14	-29.0000	*
15	39.0000	*
16	71.0000	*
17	-27.0000	*
18	87.0000	*
19	80.0000	*
20	19.0000	*
21	-156.0000	*
22	-15.0000	*
23	-90.0000	*
24	61.0000	*
25	-3.0000	*
26	-32.0000	*
27	9.0000	*
28	91.0000	*
29	-25.0000	*
30	85.0000	*
31	91.0000	*
32	6.0000	*
33	-171.0000	*
34	-5.0000	*
35	-73.0000	*
36	61.0000	*
37	-14.0000	*
38	-35.0000	*
39	22.0000	*
40	83.0000	*
41	-33.0000	*
42	82.0000	*
43	88.0000	*
44	45.0000	*
45	-185.0000	*
46	-2.0000	*
47	-92.0000	*
48	55.0000	*
49	-21.0000	*
50	-32.0000	*
51	23.0000	*
52	89.0000	*
53	-9.0000	*
54	64.0000	*
55	106.0000	*
56	12.0000	*
57	-186.0000	*
58	9.0000	*
59	-77.0000	*
60	60.0000	*
61	-21.0000	*
62	-70.0000	*
63	46.0000	*
64	58.0000	*
65	23.0000	*
66	79.0000	*
67	119.0000	*
68	3.0000	*
69	-176.0000	*
70	-21.0000	*
71	-107.0000	*
72	79.0000	*
73	-11.0000	*
74	-52.0000	*
75	24.0000	*
76	69.0000	*
77	-7.0000	*
78	94.0000	*
79	133.0000	*
80	28.0000	*
81	-221.0000	*
82	-3.0000	*
83	-110.0000	*
84	76.0000	*
85	-31.0000	*
86	-43.0000	*
87	-1.0000	*
88	108.0000	*
89	-3.0000	*
90	111.0000	*
91	113.0000	*
92	53.0000	*
93	-238.0000	*
94	-10.0000	*
95	-115.0000	*
96	78.0000	*
97	-33.0000	*
98	-39.0000	*
99	23.0000	*
100	91.0000	*
101	-11.0000	*
102	95.0000	*
103	113.0000	*
104	57.0000	*
105	-213.0000	*
106	-22.0000	*
107	-116.0000	*
108	85.0000	*
109	-37.0000	*
110	-42.0000	*
111	7.0000	*
112	79.0000	*
113	13.0000	*
114	89.0000	*
115	158.0000	*
116	45.0000	*
117	-231.0000	*
118	-16.0000	*
119	-101.0000	*
120	71.0000	*
121	-40.0000	*
122	-68.0000	*
123	3.0000	*
124	103.0000	*
125	7.0000	*
126	117.0000	*
127	182.0000	*
128	-29.0000	*
129	-226.0000	*
130	-22.0000	*
131	-98.0000	*
132	90.0000	*
133	-24.0000	*
134	-49.0000	*
135	6.0000	*
136	73.0000	*
137	6.0000	*
138	99.0000	*
139	153.0000	*
140	29.0000	*
141	-263.0000	*
142	10.0000	*
143	-108.0000	*
144	88.0000	*
145	-54.0000	*
146	-17.0000	*
147	17.0000	*
148	79.0000	*
149	-39.0000	*
150	149.0000	*
151	139.0000	*
152	49.0000	*
153	-285.0000	*
154	24.0000	*
155	-147.0000	*
156	96.0000	*
157	-2.0000	*
158	-79.0000	*
159	13.0000	*
160	99.0000	*
161	-11.0000	*
162	102.0000	*
163	175.0000	*
164	14.0000	*
165	-256.0000	*
166	-8.0000	*
167	-98.0000	*
168	115.0000	*

Auto Correlations: Room Averages

() Two Standard Error Limits

Lag	Correlation	Standard Error	-1.0000 1.0000
1	0.0190	0.0774	( ** )
2	-0.0201	0.0774	( * )
3	-0.2507	0.0774	*(** )
4	-0.0031	0.0822	( * )
5	-0.2540	0.0822	*(** )
6	0.0029	0.0867	( ** )
7	-0.2378	0.0867	(*** )
8	0.0042	0.0906	( ** )
9	-0.2221	0.0906	(**** )
10	-0.0156	0.0938	( * )
11	0.0232	0.0938	( ** )
12	0.9027	0.0938	( ****)*******************
13	0.0270	0.1362	( ** )
14	-0.0147	0.1363	( * )
15	-0.2332	0.1363	( ******* )
16	0.0039	0.1386	( ** )
17	-0.2282	0.1386	( ******* )
18	-0.0096	0.1409	( * )
19	-0.2142	0.1409	( ******* )
20	-0.0021	0.1428	( * )
21	-0.2007	0.1428	( ****** )
22	-0.0241	0.1445	( * )
23	0.0319	0.1445	( ** )
24	0.8186	0.1446	( *******)**************
25	0.0353	0.1701	( *** )

Partial Autocorrelations: Room Averages

() Two Standard Error Limits

Lag	Correlation	Standard Error	-1.0000 1.0000
1	0.0190	0.0774	( ** )
2	-0.0204	0.0774	( * )
3	-0.2501	0.0774	*(** )
4	0.0052	0.0774	( ** )
5	-0.2807	0.0774	**(** )
6	-0.0595	0.0774	( ** )
7	-0.3066	0.0774	***(** )
8	-0.1798	0.0774	(*** )
9	-0.4166	0.0774	******(** )
10	-0.5227	0.0774	*********(** )
11	-0.7529	0.0774	****************(** )
12	0.5100	0.0774	( ***)*********
13	-0.1686	0.0774	***** )
14	-0.1999	0.0774	(*** )
15	-0.0377	0.0774	( ** )
16	-0.1073	0.0774	(**** )
17	0.0794	0.0774	( **** )
18	-0.0910	0.0774	( *** )
19	0.0306	0.0774	( ** )
20	-0.0060	0.0774	( * )
21	-0.0172	0.0774	( * )
22	-0.0207	0.0774	( * )
23	-0.0014	0.0774	( * )
24	0.0452	0.0774	( *** )
25	-0.0021	0.0774	( * )

ARIMA: Fit Model

Model Results

Parameter	Estimate	Standard Error	t Ratio
(AR) P(1)	0.6641	0.0780	8.5175
(MA) Q(1)	0.9484	0.0301	31.5031

Number of Iterations	23 (Converged)

Parameter Covarience

	(AR) P(1)	(MA) Q(1)
(AR) P(1)	0.0061	-0.0021
(MA) Q(1)	-0.0021	0.0009

Parameter Correlation

	(AR) P(1)	(MA) Q(1)
(AR) P(1)	1.0000	-0.9092
(MA) Q(1)	-0.9092	1.0000

Plot of Residuals

Row	Residuals	-198.4666 220.0279
2	-13.0000	*
3	12.3161	*
4	75.0438	*
5	-11.0414	*
6	98.4531	*
7	131.5047	*
8	57.8425	*
9	-83.2057	*
10	-28.8634	*
11	-60.7916	*
12	33.5756	*
13	-13.3923	*
14	-33.7196	*
15	26.3106	*
16	70.0292	*
17	-7.8002	*
18	97.5395	*
19	114.6392	*
20	74.4884	*
21	-98.0440	*
22	-4.2969	*
23	-84.1101	*
24	41.0766	*
25	-4.5903	*
26	-34.3568	*
27	-2.3010	*
28	82.8434	*
29	-6.9407	*
30	95.0257	*
31	124.5856	*
32	63.6073	*
33	-114.7204	*
34	-0.1357	*
35	-69.8083	*
36	43.3376	*
37	-13.4482	*
38	-38.4444	*
39	8.8185	*
40	76.7456	*
41	-15.4055	*
42	89.3183	*
43	118.1704	*
44	98.5216	*
45	-121.5398	*
46	5.7002	*
47	-85.2713	*
48	35.3045	*
49	-24.0746	*
50	-40.8639	*
51	5.5340	*
52	78.9697	*
53	6.7173	*
54	76.3408	*
55	135.8281	*
56	70.2980	*
57	-127.3658	*
58	11.8445	*
59	-71.7546	*
60	43.1498	*
61	-19.9620	*
62	-74.9674	*
63	21.4574	*
64	47.7827	*
65	29.7555	*
66	91.9180	*
67	153.6256	*
68	69.5273	*
69	-112.1195	*
70	-10.3512	*
71	-102.8618	*
72	52.5996	*
73	-13.6261	*
74	-57.6052	*
75	3.9539	*
76	56.8086	*
77	1.0023	*
78	99.5980	*
79	164.9410	*
80	95.9510	*
81	-148.6862	*
82	2.8870	*
83	-105.2726	*
84	49.3077	*
85	-34.7528	*
86	-55.3402	*
87	-24.8767	*
88	85.0950	*
89	5.9034	*
90	118.5853	*
91	151.6412	*
92	121.6315	*
93	-157.9571	*
94	-1.6076	*
95	-109.8824	*
96	50.2604	*
97	-37.1782	*
98	-52.3100	*
99	-0.6620	*
100	75.0993	*
101	-0.2778	*
102	102.0415	*
103	146.5920	*
104	120.8477	*
105	-136.3559	*
106	-9.7434	*
107	-110.6219	*
108	57.2240	*
109	-39.2292	*
110	-54.5969	*
111	-16.8365	*
112	58.4000	*
113	15.8694	*
114	95.4025	*
115	189.2863	*
116	119.4151	*
117	-147.7445	*
118	-2.5802	*
119	-92.8196	*
120	50.1295	*
121	-39.6538	*
122	-79.0070	*
123	-26.6980	*
124	75.7132	*
125	10.3350	*
126	122.1434	*
127	220.0279	*
128	58.6033	*
129	-151.2192	*
130	-15.1926	*
131	-97.7847	*
132	62.4332	*
133	-24.6140	*
134	-56.3828	*
135	-14.8801	*
136	54.9177	*
137	9.5545	*
138	104.0679	*
139	185.8557	*
140	103.4851	*
141	-184.2122	*
142	10.1189	*
143	-105.0536	*
144	60.1870	*
145	-55.4140	*
146	-33.6420	*
147	-3.5846	*
148	64.3148	*
149	-30.5267	*
150	145.9763	*
151	178.3581	*
152	125.6784	*
153	-198.4666	*
154	25.2231	*
155	-139.0402	*
156	61.8853	*
157	-7.1175	*
158	-84.4153	*
159	-14.5173	*
160	76.6130	*
161	-4.1562	*
162	105.3670	*
163	207.0942	*
164	93.9979	*
165	-176.2397	*
166	-4.9761	*
167	-97.4021	*
168	87.7958	*

Residual Autocorrelations

() Two Standard Error Limits

Lag	Correlation	Standard Error	-1.0000 1.0000
1	0.1324	0.0769	( *****)
2	0.0229	0.0767	( ** )
3	-0.2246	0.0765	(** )
4	-0.0713	0.0762	( *** )
5	-0.3178	0.0760	***(** )
6	-0.0959	0.0757	( *** )
7	-0.2863	0.0755	**(** )
8	-0.0590	0.0753	( ** )
9	-0.2078	0.0750	(** )
10	0.0295	0.0748	( ** )
11	0.1221	0.0746	( *****)
12	0.9066	0.0743	( ***)********************
13	0.1338	0.0741	( *****)
14	0.0237	0.0738	( ** )
15	-0.2052	0.0736	(** )
16	-0.0612	0.0733	( ** )
17	-0.2864	0.0731	**(** )
18	-0.1024	0.0728	(**** )
19	-0.2584	0.0726	*(** )
20	-0.0601	0.0724	( ** )
21	-0.1896	0.0721	(*** )
22	0.0151	0.0719	( ** )
23	0.1242	0.0716	( *****)
24	0.8237	0.0714	( ***)******************
25	0.1313	0.0711	( *****)

Ljung-Box Statistic

	Lag	Ljung Box
6	31.6452	4
12	205.9937	10
18	235.1639	16
24	391.7445	22
25	395.1525	23

ARIMA: Forecasting

Forecast Table: Room Averages

Forecasts with Origin at 168

Row	Forecast	Lower 95%	Upper 95%
169	870.0984	701.5883	1038.6085
170	865.5153	633.2687	1097.7620
171	862.4719	630.2252	1094.7185
172	860.4508	628.2042	1092.6974
173	859.1087	626.8621	1091.3553
174	858.2175	625.9708	1090.4641
175	857.6256	625.3790	1089.8723
176	857.2326	624.9860	1089.4792
177	856.9716	624.7250	1089.2183
178	856.7983	624.5517	1089.0449
179	856.6832	624.4366	1088.9299
180	856.6068	624.3601	1088.8534
181	856.5560	624.3094	1088.8027
182	856.5223	624.2757	1088.7690
183	856.5000	624.2533	1088.7466
184	856.4851	624.2384	1088.7317
185	856.4752	624.2286	1088.7219
186	856.4687	624.2220	1088.7153
187	856.4643	624.2177	1088.7110
188	856.4614	624.2148	1088.7081
189	856.4595	624.2129	1088.7061
190	856.4582	624.2116	1088.7049
191	856.4574	624.2107	1088.7040
192	856.4568	624.2102	1088.7035

Character Forecast Plot: Room Averages

* - Data
() - 95% Estimated Confidence Limits
+ - Lead 1 Forcasts
O - Forecasts with Origin at 168

Row	480.0000 1125.0000
1	*
2	*+ )
3	+* )
4	+ * )
5	*+ )
6	+ * )
7	+ * )
8	( + * )
9	( * + )
10	* + )
11	* + )
12	+ * )
13	* + )
14	* + )
15	+ * )
16	+ * )
17	*+ )
18	+ * )
19	+ * )
20	( + * )
21	( * + )
22	* )
23	* + )
24	+ * )
25	* )
26	* + )
27	* )
28	+ * )
29	* )
30	+ * )
31	( + * )
32	( + * )
33	( * + )
34	* )
35	* + )
36	+ * )
37	*+ )
38	* + )
39	+* )
40	+ * )
41	* + )
42	+ * )
43	( + * )
44	( + * )
45	( * + )
46	+* )
47	* + )
48	+ * )
49	* + )
50	* + )
51	+* )
52	+ * )
53	( +* )
54	( + * )
55	( + * )
56	( + * )
57	( * + )
58	( + * )
59	( * + )
60	+ * )
61	* + )
62	* + )
63	+ * )
64	+ * )
65	( + * )
66	( + * )
67	( + * )
68	( + * )
69	( * + )
70	( *+ )
71	( * + )
72	+ * )
73	( *+ )
74	( * + )
75	+* )
76	+ * )
77	( * )
78	( + * )
79	( + *
80	( + * )
81	( * + )
82	( * )
83	( * + )
84	+ * )
85	( * + )
86	( * + )
87	* + )
88	+ * )
89	( +* )
90	( + * )
91	( + * )
92	( + * )
93	(* + )
94	( * )
95	( * + )
96	( + * )
97	( * + )
98	( * + )
99	( *+ )
100	( + * )
101	( * )
102	( + * )
103	( + * )
104	( + * )
105	( * + )
106	( * )
107	( * + )
108	( + * )
109	( * + )
110	( * + )
111	( * + )
112	( + * )
113	( + * )
114	( + * )
115	( + ) *
116	( + * )
117	( * + )
118	( * )
119	( * + )
120	( + * )
121	( * + )
122	( * + )
123	( * + )
124	( + * )
125	( +* )
126	( + * )
127	( + ) *
128	( + *
129	(* +
130	( * + )
131	( * + )
132	( + * )
133	( * + )
134	( * + )
135	( * + )
136	( + * )
137	( +* )
138	( + * )
139	( + ) *
140	( + *
141	* ( +
142	( +* )
143	( * + )
144	( + * )
145	( * + )
146	( * + )
147	( * )
148	( + * )
149	( * + )
150	( + * )
151	( + )*
152	( + *
153	* ( +
154	( + * )
155	( * + )
156	( + * )
157	( *+ )
158	( * + )
159	( * + )
160	( + * )
161	( *+ )
162	( + * )
163	( + ) *
164	( + *
165	*( +
166	( * )
167	( * + )
168	( + * )
169	( O )
170	( O )
171	( O )
172	( O )
173	( O )
174	( O )
175	( O )
176	( O )
177	( O )
178	( O )
179	( O )
180	( O )
181	( O )
182	( O )
183	( O )
184	( O )
185	( O )
186	( O )
187	( O )
188	( O )
189	( O )
190	( O )
191	( O )
192	( O )

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