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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Thu, 18 Dec 2008 09:01:41 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/18/t122961612876vz9kpd92t5b81.htm/, Retrieved Sat, 11 May 2024 05:06:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34865, Retrieved Sat, 11 May 2024 05:06:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

200

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Variance Reduction Matrix] [] [2008-11-30 18:13:06] [b745fd448f60064800b631a75a630267]
F RM D    [Standard Deviation-Mean Plot] [SMP Q1] [2008-12-07 13:12:10] [e5d91604aae608e98a8ea24759233f66]
F RM        [Variance Reduction Matrix] [VRM Q1] [2008-12-07 13:13:31] [e5d91604aae608e98a8ea24759233f66]
F RMP         [(Partial) Autocorrelation Function] [ACF Q2] [2008-12-07 13:20:49] [e5d91604aae608e98a8ea24759233f66]
F RMP           [ARIMA Backward Selection] [ARMA Q5] [2008-12-07 13:46:58] [e5d91604aae608e98a8ea24759233f66]
F RMPD            [ARIMA Forecasting] [Forecasting Infla...] [2008-12-10 18:36:07] [e5d91604aae608e98a8ea24759233f66]
-   P                 [ARIMA Forecasting] [Forecasting] [2008-12-18 16:01:41] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]

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Dataseries X:

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Histogram

Boxplots

0.42
0.74
1.02
1.51
1.86
1.59
1.03
0.44
0.82
0.86
0.57
0.59
0.95
0.98
1.23
1.17
0.84
0.74
0.65
0.91
1.19
1.3
1.53
1.94
1.79
1.95
2.26
2.04
2.16
2.75
2.79
2.88
3.36
2.97
3.1
2.49
2.2
2.25
2.09
2.79
3.14
2.93
2.65
2.67
2.26
2.35
2.13
2.18
2.9
2.63
2.67
1.81
1.33
0.88
1.28
1.26
1.26
1.29
1.1
1.37
1.21
1.74
1.76
1.48
1.04
1.62
1.49
1.79
1.8
1.58
1.86
1.74
1.59
1.26
1.13
1.92
2.61
2.26
2.41
2.26
2.03
2.86
2.55
2.27
2.26
2.57
3.07
2.76
2.51
2.87
3.14
3.11
3.16
2.47
2.57
2.89
2.63
2.38
1.69
1.96
2.19
1.87
1.6
1.63
1.22
1.21
1.49
1.64
1.66
1.77
1.82
1.78
1.28
1.29
1.37
1.12
1.51
2.24
2.94
3.09

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34865&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34865&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34865&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[108])
96	2.89	-	-	-	-	-	-	-
97	2.63	-	-	-	-	-	-	-
98	2.38	-	-	-	-	-	-	-
99	1.69	-	-	-	-	-	-	-
100	1.96	-	-	-	-	-	-	-
101	2.19	-	-	-	-	-	-	-
102	1.87	-	-	-	-	-	-	-
103	1.6	-	-	-	-	-	-	-
104	1.63	-	-	-	-	-	-	-
105	1.22	-	-	-	-	-	-	-
106	1.21	-	-	-	-	-	-	-
107	1.49	-	-	-	-	-	-	-
108	1.64	-	-	-	-	-	-	-
109	1.66	1.8749	1.3697	2.3801	0.2022	0.8189	0.0017	0.8189
110	1.77	1.7683	1.0078	2.5288	0.4983	0.6099	0.0575	0.6296
111	1.82	1.9175	1.0147	2.8203	0.4162	0.6256	0.6893	0.7266
112	1.78	1.7074	0.713	2.7018	0.4431	0.4122	0.3093	0.5528
113	1.28	1.5764	0.5077	2.6451	0.2934	0.3544	0.1302	0.4536
114	1.29	1.6546	0.5161	2.7931	0.2651	0.7405	0.3554	0.51
115	1.37	1.6296	0.4231	2.8361	0.3366	0.7094	0.5192	0.4933
116	1.12	1.5329	0.2607	2.8051	0.2623	0.5991	0.4405	0.4345
117	1.51	1.9417	0.6068	3.2766	0.2631	0.8862	0.8554	0.6711
118	2.24	2.0953	0.7004	3.4901	0.4194	0.7946	0.8932	0.7388
119	2.94	1.948	0.4956	3.4004	0.0903	0.3468	0.7317	0.6612
120	3.09	1.7853	0.2775	3.2931	0.0449	0.0667	0.5749	0.5749

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[108]) \tabularnewline
96 & 2.89 & - & - & - & - & - & - & - \tabularnewline
97 & 2.63 & - & - & - & - & - & - & - \tabularnewline
98 & 2.38 & - & - & - & - & - & - & - \tabularnewline
99 & 1.69 & - & - & - & - & - & - & - \tabularnewline
100 & 1.96 & - & - & - & - & - & - & - \tabularnewline
101 & 2.19 & - & - & - & - & - & - & - \tabularnewline
102 & 1.87 & - & - & - & - & - & - & - \tabularnewline
103 & 1.6 & - & - & - & - & - & - & - \tabularnewline
104 & 1.63 & - & - & - & - & - & - & - \tabularnewline
105 & 1.22 & - & - & - & - & - & - & - \tabularnewline
106 & 1.21 & - & - & - & - & - & - & - \tabularnewline
107 & 1.49 & - & - & - & - & - & - & - \tabularnewline
108 & 1.64 & - & - & - & - & - & - & - \tabularnewline
109 & 1.66 & 1.8749 & 1.3697 & 2.3801 & 0.2022 & 0.8189 & 0.0017 & 0.8189 \tabularnewline
110 & 1.77 & 1.7683 & 1.0078 & 2.5288 & 0.4983 & 0.6099 & 0.0575 & 0.6296 \tabularnewline
111 & 1.82 & 1.9175 & 1.0147 & 2.8203 & 0.4162 & 0.6256 & 0.6893 & 0.7266 \tabularnewline
112 & 1.78 & 1.7074 & 0.713 & 2.7018 & 0.4431 & 0.4122 & 0.3093 & 0.5528 \tabularnewline
113 & 1.28 & 1.5764 & 0.5077 & 2.6451 & 0.2934 & 0.3544 & 0.1302 & 0.4536 \tabularnewline
114 & 1.29 & 1.6546 & 0.5161 & 2.7931 & 0.2651 & 0.7405 & 0.3554 & 0.51 \tabularnewline
115 & 1.37 & 1.6296 & 0.4231 & 2.8361 & 0.3366 & 0.7094 & 0.5192 & 0.4933 \tabularnewline
116 & 1.12 & 1.5329 & 0.2607 & 2.8051 & 0.2623 & 0.5991 & 0.4405 & 0.4345 \tabularnewline
117 & 1.51 & 1.9417 & 0.6068 & 3.2766 & 0.2631 & 0.8862 & 0.8554 & 0.6711 \tabularnewline
118 & 2.24 & 2.0953 & 0.7004 & 3.4901 & 0.4194 & 0.7946 & 0.8932 & 0.7388 \tabularnewline
119 & 2.94 & 1.948 & 0.4956 & 3.4004 & 0.0903 & 0.3468 & 0.7317 & 0.6612 \tabularnewline
120 & 3.09 & 1.7853 & 0.2775 & 3.2931 & 0.0449 & 0.0667 & 0.5749 & 0.5749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34865&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[108])[/C][/ROW]
[ROW][C]96[/C][C]2.89[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]97[/C][C]2.63[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]98[/C][C]2.38[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]99[/C][C]1.69[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]100[/C][C]1.96[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]101[/C][C]2.19[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]102[/C][C]1.87[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]103[/C][C]1.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]104[/C][C]1.63[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]105[/C][C]1.22[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]106[/C][C]1.21[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]107[/C][C]1.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]108[/C][C]1.64[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]109[/C][C]1.66[/C][C]1.8749[/C][C]1.3697[/C][C]2.3801[/C][C]0.2022[/C][C]0.8189[/C][C]0.0017[/C][C]0.8189[/C][/ROW]
[ROW][C]110[/C][C]1.77[/C][C]1.7683[/C][C]1.0078[/C][C]2.5288[/C][C]0.4983[/C][C]0.6099[/C][C]0.0575[/C][C]0.6296[/C][/ROW]
[ROW][C]111[/C][C]1.82[/C][C]1.9175[/C][C]1.0147[/C][C]2.8203[/C][C]0.4162[/C][C]0.6256[/C][C]0.6893[/C][C]0.7266[/C][/ROW]
[ROW][C]112[/C][C]1.78[/C][C]1.7074[/C][C]0.713[/C][C]2.7018[/C][C]0.4431[/C][C]0.4122[/C][C]0.3093[/C][C]0.5528[/C][/ROW]
[ROW][C]113[/C][C]1.28[/C][C]1.5764[/C][C]0.5077[/C][C]2.6451[/C][C]0.2934[/C][C]0.3544[/C][C]0.1302[/C][C]0.4536[/C][/ROW]
[ROW][C]114[/C][C]1.29[/C][C]1.6546[/C][C]0.5161[/C][C]2.7931[/C][C]0.2651[/C][C]0.7405[/C][C]0.3554[/C][C]0.51[/C][/ROW]
[ROW][C]115[/C][C]1.37[/C][C]1.6296[/C][C]0.4231[/C][C]2.8361[/C][C]0.3366[/C][C]0.7094[/C][C]0.5192[/C][C]0.4933[/C][/ROW]
[ROW][C]116[/C][C]1.12[/C][C]1.5329[/C][C]0.2607[/C][C]2.8051[/C][C]0.2623[/C][C]0.5991[/C][C]0.4405[/C][C]0.4345[/C][/ROW]
[ROW][C]117[/C][C]1.51[/C][C]1.9417[/C][C]0.6068[/C][C]3.2766[/C][C]0.2631[/C][C]0.8862[/C][C]0.8554[/C][C]0.6711[/C][/ROW]
[ROW][C]118[/C][C]2.24[/C][C]2.0953[/C][C]0.7004[/C][C]3.4901[/C][C]0.4194[/C][C]0.7946[/C][C]0.8932[/C][C]0.7388[/C][/ROW]
[ROW][C]119[/C][C]2.94[/C][C]1.948[/C][C]0.4956[/C][C]3.4004[/C][C]0.0903[/C][C]0.3468[/C][C]0.7317[/C][C]0.6612[/C][/ROW]
[ROW][C]120[/C][C]3.09[/C][C]1.7853[/C][C]0.2775[/C][C]3.2931[/C][C]0.0449[/C][C]0.0667[/C][C]0.5749[/C][C]0.5749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34865&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34865&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[108])
96	2.89	-	-	-	-	-	-	-
97	2.63	-	-	-	-	-	-	-
98	2.38	-	-	-	-	-	-	-
99	1.69	-	-	-	-	-	-	-
100	1.96	-	-	-	-	-	-	-
101	2.19	-	-	-	-	-	-	-
102	1.87	-	-	-	-	-	-	-
103	1.6	-	-	-	-	-	-	-
104	1.63	-	-	-	-	-	-	-
105	1.22	-	-	-	-	-	-	-
106	1.21	-	-	-	-	-	-	-
107	1.49	-	-	-	-	-	-	-
108	1.64	-	-	-	-	-	-	-
109	1.66	1.8749	1.3697	2.3801	0.2022	0.8189	0.0017	0.8189
110	1.77	1.7683	1.0078	2.5288	0.4983	0.6099	0.0575	0.6296
111	1.82	1.9175	1.0147	2.8203	0.4162	0.6256	0.6893	0.7266
112	1.78	1.7074	0.713	2.7018	0.4431	0.4122	0.3093	0.5528
113	1.28	1.5764	0.5077	2.6451	0.2934	0.3544	0.1302	0.4536
114	1.29	1.6546	0.5161	2.7931	0.2651	0.7405	0.3554	0.51
115	1.37	1.6296	0.4231	2.8361	0.3366	0.7094	0.5192	0.4933
116	1.12	1.5329	0.2607	2.8051	0.2623	0.5991	0.4405	0.4345
117	1.51	1.9417	0.6068	3.2766	0.2631	0.8862	0.8554	0.6711
118	2.24	2.0953	0.7004	3.4901	0.4194	0.7946	0.8932	0.7388
119	2.94	1.948	0.4956	3.4004	0.0903	0.3468	0.7317	0.6612
120	3.09	1.7853	0.2775	3.2931	0.0449	0.0667	0.5749	0.5749

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
109	0.1375	-0.1146	0.0096	0.0462	0.0038	0.062
110	0.2194	0.001	1e-04	0	0	5e-04
111	0.2402	-0.0508	0.0042	0.0095	8e-04	0.0281
112	0.2971	0.0425	0.0035	0.0053	4e-04	0.021
113	0.3459	-0.188	0.0157	0.0879	0.0073	0.0856
114	0.3511	-0.2204	0.0184	0.1329	0.0111	0.1053
115	0.3777	-0.1593	0.0133	0.0674	0.0056	0.0749
116	0.4234	-0.2694	0.0224	0.1705	0.0142	0.1192
117	0.3508	-0.2223	0.0185	0.1864	0.0155	0.1246
118	0.3396	0.0691	0.0058	0.0209	0.0017	0.0418
119	0.3804	0.5092	0.0424	0.9841	0.082	0.2864
120	0.4309	0.7308	0.0609	1.7023	0.1419	0.3766

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
109 & 0.1375 & -0.1146 & 0.0096 & 0.0462 & 0.0038 & 0.062 \tabularnewline
110 & 0.2194 & 0.001 & 1e-04 & 0 & 0 & 5e-04 \tabularnewline
111 & 0.2402 & -0.0508 & 0.0042 & 0.0095 & 8e-04 & 0.0281 \tabularnewline
112 & 0.2971 & 0.0425 & 0.0035 & 0.0053 & 4e-04 & 0.021 \tabularnewline
113 & 0.3459 & -0.188 & 0.0157 & 0.0879 & 0.0073 & 0.0856 \tabularnewline
114 & 0.3511 & -0.2204 & 0.0184 & 0.1329 & 0.0111 & 0.1053 \tabularnewline
115 & 0.3777 & -0.1593 & 0.0133 & 0.0674 & 0.0056 & 0.0749 \tabularnewline
116 & 0.4234 & -0.2694 & 0.0224 & 0.1705 & 0.0142 & 0.1192 \tabularnewline
117 & 0.3508 & -0.2223 & 0.0185 & 0.1864 & 0.0155 & 0.1246 \tabularnewline
118 & 0.3396 & 0.0691 & 0.0058 & 0.0209 & 0.0017 & 0.0418 \tabularnewline
119 & 0.3804 & 0.5092 & 0.0424 & 0.9841 & 0.082 & 0.2864 \tabularnewline
120 & 0.4309 & 0.7308 & 0.0609 & 1.7023 & 0.1419 & 0.3766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34865&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]109[/C][C]0.1375[/C][C]-0.1146[/C][C]0.0096[/C][C]0.0462[/C][C]0.0038[/C][C]0.062[/C][/ROW]
[ROW][C]110[/C][C]0.2194[/C][C]0.001[/C][C]1e-04[/C][C]0[/C][C]0[/C][C]5e-04[/C][/ROW]
[ROW][C]111[/C][C]0.2402[/C][C]-0.0508[/C][C]0.0042[/C][C]0.0095[/C][C]8e-04[/C][C]0.0281[/C][/ROW]
[ROW][C]112[/C][C]0.2971[/C][C]0.0425[/C][C]0.0035[/C][C]0.0053[/C][C]4e-04[/C][C]0.021[/C][/ROW]
[ROW][C]113[/C][C]0.3459[/C][C]-0.188[/C][C]0.0157[/C][C]0.0879[/C][C]0.0073[/C][C]0.0856[/C][/ROW]
[ROW][C]114[/C][C]0.3511[/C][C]-0.2204[/C][C]0.0184[/C][C]0.1329[/C][C]0.0111[/C][C]0.1053[/C][/ROW]
[ROW][C]115[/C][C]0.3777[/C][C]-0.1593[/C][C]0.0133[/C][C]0.0674[/C][C]0.0056[/C][C]0.0749[/C][/ROW]
[ROW][C]116[/C][C]0.4234[/C][C]-0.2694[/C][C]0.0224[/C][C]0.1705[/C][C]0.0142[/C][C]0.1192[/C][/ROW]
[ROW][C]117[/C][C]0.3508[/C][C]-0.2223[/C][C]0.0185[/C][C]0.1864[/C][C]0.0155[/C][C]0.1246[/C][/ROW]
[ROW][C]118[/C][C]0.3396[/C][C]0.0691[/C][C]0.0058[/C][C]0.0209[/C][C]0.0017[/C][C]0.0418[/C][/ROW]
[ROW][C]119[/C][C]0.3804[/C][C]0.5092[/C][C]0.0424[/C][C]0.9841[/C][C]0.082[/C][C]0.2864[/C][/ROW]
[ROW][C]120[/C][C]0.4309[/C][C]0.7308[/C][C]0.0609[/C][C]1.7023[/C][C]0.1419[/C][C]0.3766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34865&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34865&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
109	0.1375	-0.1146	0.0096	0.0462	0.0038	0.062
110	0.2194	0.001	1e-04	0	0	5e-04
111	0.2402	-0.0508	0.0042	0.0095	8e-04	0.0281
112	0.2971	0.0425	0.0035	0.0053	4e-04	0.021
113	0.3459	-0.188	0.0157	0.0879	0.0073	0.0856
114	0.3511	-0.2204	0.0184	0.1329	0.0111	0.1053
115	0.3777	-0.1593	0.0133	0.0674	0.0056	0.0749
116	0.4234	-0.2694	0.0224	0.1705	0.0142	0.1192
117	0.3508	-0.2223	0.0185	0.1864	0.0155	0.1246
118	0.3396	0.0691	0.0058	0.0209	0.0017	0.0418
119	0.3804	0.5092	0.0424	0.9841	0.082	0.2864
120	0.4309	0.7308	0.0609	1.7023	0.1419	0.3766

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1.3 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,fx))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:12] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code