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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Tue, 18 Dec 2012 16:14:33 -0500

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/2012/Dec/18/t1355865289ybdt8dkz9141eig.htm/, Retrieved Fri, 01 Nov 2024 00:18:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201666, Retrieved Fri, 01 Nov 2024 00:18:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

149

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

-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Soldiers] [2010-11-29 09:51:25] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Soldiers] [2010-11-29 11:02:42] [b98453cac15ba1066b407e146608df68]
- RMP       [ARIMA Forecasting] [Soldiers] [2010-11-29 21:04:02] [b98453cac15ba1066b407e146608df68]
-   PD        [ARIMA Forecasting] [] [2010-12-15 17:27:57] [8d263c682820d5327cb5f02a8c3630cf]
F   PD          [ARIMA Forecasting] [] [2010-12-17 08:37:05] [4dfa50539945b119a90a7606969443b9]
- R P             [ARIMA Forecasting] [forecasting ] [2012-12-02 20:11:28] [885d0a915dae889a27a534b235a2244f]
-   P                 [ARIMA Forecasting] [ARIMA Forecast] [2012-12-18 21:14:33] [f2ee352554ba43a37c941acf183fae36] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201666&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201666&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201666&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

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[60])
48	872705	-	-	-	-	-	-	-
49	628151	-	-	-	-	-	-	-
50	953712	-	-	-	-	-	-	-
51	1160384	-	-	-	-	-	-	-
52	1400618	-	-	-	-	-	-	-
53	1661511	-	-	-	-	-	-	-
54	1495347	-	-	-	-	-	-	-
55	2918786	-	-	-	-	-	-	-
56	2775677	-	-	-	-	-	-	-
57	1407026	-	-	-	-	-	-	-
58	1370199	-	-	-	-	-	-	-
59	964526	-	-	-	-	-	-	-
60	850851	-	-	-	-	-	-	-
61	683118	647398.005	477810.8705	816985.1395	0.3399	0.0094	0.588	0.0094
62	847224	899185.9224	724760.8125	1073611.0322	0.2796	0.9924	0.27	0.7065
63	1073256	1133175.5792	958460.4745	1307890.6838	0.2507	0.9993	0.3801	0.9992
64	1514326	1532111.9233	1357379.1923	1706844.6542	0.4209	1	0.9299	1
65	1503734	1618958.927	1444225.1239	1793692.7302	0.0981	0.8797	0.3166	1
66	1507712	1535225.4381	1360491.5697	1709959.3065	0.3788	0.638	0.6727	1
67	2865698	2997797.1999	2823063.3277	3172531.0721	0.0692	1	0.8123	1
68	2788128	2654093.2492	2479359.3788	2828827.1195	0.0664	0.0088	0.0863	1
69	1391596	1377959.2934	1203225.4582	1552693.1287	0.4392	0	0.3722	1
70	1366378	1358264.317	1183531.0581	1532997.5758	0.4637	0.3542	0.4468	1
71	946295	961236.2254	786512.4422	1135960.0085	0.4334	0	0.4853	0.8922
72	859626	860726.0551	686158.1075	1035294.0028	0.4951	0.1683	0.5441	0.5441

\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[60]) \tabularnewline
48 & 872705 & - & - & - & - & - & - & - \tabularnewline
49 & 628151 & - & - & - & - & - & - & - \tabularnewline
50 & 953712 & - & - & - & - & - & - & - \tabularnewline
51 & 1160384 & - & - & - & - & - & - & - \tabularnewline
52 & 1400618 & - & - & - & - & - & - & - \tabularnewline
53 & 1661511 & - & - & - & - & - & - & - \tabularnewline
54 & 1495347 & - & - & - & - & - & - & - \tabularnewline
55 & 2918786 & - & - & - & - & - & - & - \tabularnewline
56 & 2775677 & - & - & - & - & - & - & - \tabularnewline
57 & 1407026 & - & - & - & - & - & - & - \tabularnewline
58 & 1370199 & - & - & - & - & - & - & - \tabularnewline
59 & 964526 & - & - & - & - & - & - & - \tabularnewline
60 & 850851 & - & - & - & - & - & - & - \tabularnewline
61 & 683118 & 647398.005 & 477810.8705 & 816985.1395 & 0.3399 & 0.0094 & 0.588 & 0.0094 \tabularnewline
62 & 847224 & 899185.9224 & 724760.8125 & 1073611.0322 & 0.2796 & 0.9924 & 0.27 & 0.7065 \tabularnewline
63 & 1073256 & 1133175.5792 & 958460.4745 & 1307890.6838 & 0.2507 & 0.9993 & 0.3801 & 0.9992 \tabularnewline
64 & 1514326 & 1532111.9233 & 1357379.1923 & 1706844.6542 & 0.4209 & 1 & 0.9299 & 1 \tabularnewline
65 & 1503734 & 1618958.927 & 1444225.1239 & 1793692.7302 & 0.0981 & 0.8797 & 0.3166 & 1 \tabularnewline
66 & 1507712 & 1535225.4381 & 1360491.5697 & 1709959.3065 & 0.3788 & 0.638 & 0.6727 & 1 \tabularnewline
67 & 2865698 & 2997797.1999 & 2823063.3277 & 3172531.0721 & 0.0692 & 1 & 0.8123 & 1 \tabularnewline
68 & 2788128 & 2654093.2492 & 2479359.3788 & 2828827.1195 & 0.0664 & 0.0088 & 0.0863 & 1 \tabularnewline
69 & 1391596 & 1377959.2934 & 1203225.4582 & 1552693.1287 & 0.4392 & 0 & 0.3722 & 1 \tabularnewline
70 & 1366378 & 1358264.317 & 1183531.0581 & 1532997.5758 & 0.4637 & 0.3542 & 0.4468 & 1 \tabularnewline
71 & 946295 & 961236.2254 & 786512.4422 & 1135960.0085 & 0.4334 & 0 & 0.4853 & 0.8922 \tabularnewline
72 & 859626 & 860726.0551 & 686158.1075 & 1035294.0028 & 0.4951 & 0.1683 & 0.5441 & 0.5441 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201666&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[60])[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]647398.005[/C][C]477810.8705[/C][C]816985.1395[/C][C]0.3399[/C][C]0.0094[/C][C]0.588[/C][C]0.0094[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]899185.9224[/C][C]724760.8125[/C][C]1073611.0322[/C][C]0.2796[/C][C]0.9924[/C][C]0.27[/C][C]0.7065[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]1133175.5792[/C][C]958460.4745[/C][C]1307890.6838[/C][C]0.2507[/C][C]0.9993[/C][C]0.3801[/C][C]0.9992[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1532111.9233[/C][C]1357379.1923[/C][C]1706844.6542[/C][C]0.4209[/C][C]1[/C][C]0.9299[/C][C]1[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1618958.927[/C][C]1444225.1239[/C][C]1793692.7302[/C][C]0.0981[/C][C]0.8797[/C][C]0.3166[/C][C]1[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1535225.4381[/C][C]1360491.5697[/C][C]1709959.3065[/C][C]0.3788[/C][C]0.638[/C][C]0.6727[/C][C]1[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]2997797.1999[/C][C]2823063.3277[/C][C]3172531.0721[/C][C]0.0692[/C][C]1[/C][C]0.8123[/C][C]1[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2654093.2492[/C][C]2479359.3788[/C][C]2828827.1195[/C][C]0.0664[/C][C]0.0088[/C][C]0.0863[/C][C]1[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]1377959.2934[/C][C]1203225.4582[/C][C]1552693.1287[/C][C]0.4392[/C][C]0[/C][C]0.3722[/C][C]1[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1358264.317[/C][C]1183531.0581[/C][C]1532997.5758[/C][C]0.4637[/C][C]0.3542[/C][C]0.4468[/C][C]1[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]961236.2254[/C][C]786512.4422[/C][C]1135960.0085[/C][C]0.4334[/C][C]0[/C][C]0.4853[/C][C]0.8922[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]860726.0551[/C][C]686158.1075[/C][C]1035294.0028[/C][C]0.4951[/C][C]0.1683[/C][C]0.5441[/C][C]0.5441[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201666&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201666&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[60])
48	872705	-	-	-	-	-	-	-
49	628151	-	-	-	-	-	-	-
50	953712	-	-	-	-	-	-	-
51	1160384	-	-	-	-	-	-	-
52	1400618	-	-	-	-	-	-	-
53	1661511	-	-	-	-	-	-	-
54	1495347	-	-	-	-	-	-	-
55	2918786	-	-	-	-	-	-	-
56	2775677	-	-	-	-	-	-	-
57	1407026	-	-	-	-	-	-	-
58	1370199	-	-	-	-	-	-	-
59	964526	-	-	-	-	-	-	-
60	850851	-	-	-	-	-	-	-
61	683118	647398.005	477810.8705	816985.1395	0.3399	0.0094	0.588	0.0094
62	847224	899185.9224	724760.8125	1073611.0322	0.2796	0.9924	0.27	0.7065
63	1073256	1133175.5792	958460.4745	1307890.6838	0.2507	0.9993	0.3801	0.9992
64	1514326	1532111.9233	1357379.1923	1706844.6542	0.4209	1	0.9299	1
65	1503734	1618958.927	1444225.1239	1793692.7302	0.0981	0.8797	0.3166	1
66	1507712	1535225.4381	1360491.5697	1709959.3065	0.3788	0.638	0.6727	1
67	2865698	2997797.1999	2823063.3277	3172531.0721	0.0692	1	0.8123	1
68	2788128	2654093.2492	2479359.3788	2828827.1195	0.0664	0.0088	0.0863	1
69	1391596	1377959.2934	1203225.4582	1552693.1287	0.4392	0	0.3722	1
70	1366378	1358264.317	1183531.0581	1532997.5758	0.4637	0.3542	0.4468	1
71	946295	961236.2254	786512.4422	1135960.0085	0.4334	0	0.4853	0.8922
72	859626	860726.0551	686158.1075	1035294.0028	0.4951	0.1683	0.5441	0.5441

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.1336	0.0552	0	1275918041.6984	0	0
62	0.099	-0.0578	0.0565	2700041376.0511	1987979708.8747	44586.7661
63	0.0787	-0.0529	0.0553	3590355967.9129	2522105128.5541	50220.5648
64	0.0582	-0.0116	0.0444	316339066.1667	1970663612.9573	44392.1571
65	0.0551	-0.0712	0.0497	13276783805.5145	4231887651.4687	65052.9604
66	0.0581	-0.0179	0.0444	756989276.2136	3652737922.2595	60437.8848
67	0.0297	-0.0441	0.0444	17450198614.7012	5623803735.4655	74992.0245
68	0.0336	0.0505	0.0451	17965314429.7776	7166492572.2545	84655.1391
69	0.0647	0.0099	0.0412	185959766.1334	6390877816.0188	79942.966
70	0.0656	0.006	0.0377	65831852.2171	5758373219.6387	75883.9457
71	0.0927	-0.0155	0.0357	223240214.9774	5255179310.124	72492.6156
72	0.1035	-0.0013	0.0328	1210121.258	4817348544.3852	69407.1217

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.1336 & 0.0552 & 0 & 1275918041.6984 & 0 & 0 \tabularnewline
62 & 0.099 & -0.0578 & 0.0565 & 2700041376.0511 & 1987979708.8747 & 44586.7661 \tabularnewline
63 & 0.0787 & -0.0529 & 0.0553 & 3590355967.9129 & 2522105128.5541 & 50220.5648 \tabularnewline
64 & 0.0582 & -0.0116 & 0.0444 & 316339066.1667 & 1970663612.9573 & 44392.1571 \tabularnewline
65 & 0.0551 & -0.0712 & 0.0497 & 13276783805.5145 & 4231887651.4687 & 65052.9604 \tabularnewline
66 & 0.0581 & -0.0179 & 0.0444 & 756989276.2136 & 3652737922.2595 & 60437.8848 \tabularnewline
67 & 0.0297 & -0.0441 & 0.0444 & 17450198614.7012 & 5623803735.4655 & 74992.0245 \tabularnewline
68 & 0.0336 & 0.0505 & 0.0451 & 17965314429.7776 & 7166492572.2545 & 84655.1391 \tabularnewline
69 & 0.0647 & 0.0099 & 0.0412 & 185959766.1334 & 6390877816.0188 & 79942.966 \tabularnewline
70 & 0.0656 & 0.006 & 0.0377 & 65831852.2171 & 5758373219.6387 & 75883.9457 \tabularnewline
71 & 0.0927 & -0.0155 & 0.0357 & 223240214.9774 & 5255179310.124 & 72492.6156 \tabularnewline
72 & 0.1035 & -0.0013 & 0.0328 & 1210121.258 & 4817348544.3852 & 69407.1217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201666&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]61[/C][C]0.1336[/C][C]0.0552[/C][C]0[/C][C]1275918041.6984[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.099[/C][C]-0.0578[/C][C]0.0565[/C][C]2700041376.0511[/C][C]1987979708.8747[/C][C]44586.7661[/C][/ROW]
[ROW][C]63[/C][C]0.0787[/C][C]-0.0529[/C][C]0.0553[/C][C]3590355967.9129[/C][C]2522105128.5541[/C][C]50220.5648[/C][/ROW]
[ROW][C]64[/C][C]0.0582[/C][C]-0.0116[/C][C]0.0444[/C][C]316339066.1667[/C][C]1970663612.9573[/C][C]44392.1571[/C][/ROW]
[ROW][C]65[/C][C]0.0551[/C][C]-0.0712[/C][C]0.0497[/C][C]13276783805.5145[/C][C]4231887651.4687[/C][C]65052.9604[/C][/ROW]
[ROW][C]66[/C][C]0.0581[/C][C]-0.0179[/C][C]0.0444[/C][C]756989276.2136[/C][C]3652737922.2595[/C][C]60437.8848[/C][/ROW]
[ROW][C]67[/C][C]0.0297[/C][C]-0.0441[/C][C]0.0444[/C][C]17450198614.7012[/C][C]5623803735.4655[/C][C]74992.0245[/C][/ROW]
[ROW][C]68[/C][C]0.0336[/C][C]0.0505[/C][C]0.0451[/C][C]17965314429.7776[/C][C]7166492572.2545[/C][C]84655.1391[/C][/ROW]
[ROW][C]69[/C][C]0.0647[/C][C]0.0099[/C][C]0.0412[/C][C]185959766.1334[/C][C]6390877816.0188[/C][C]79942.966[/C][/ROW]
[ROW][C]70[/C][C]0.0656[/C][C]0.006[/C][C]0.0377[/C][C]65831852.2171[/C][C]5758373219.6387[/C][C]75883.9457[/C][/ROW]
[ROW][C]71[/C][C]0.0927[/C][C]-0.0155[/C][C]0.0357[/C][C]223240214.9774[/C][C]5255179310.124[/C][C]72492.6156[/C][/ROW]
[ROW][C]72[/C][C]0.1035[/C][C]-0.0013[/C][C]0.0328[/C][C]1210121.258[/C][C]4817348544.3852[/C][C]69407.1217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201666&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201666&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
61	0.1336	0.0552	0	1275918041.6984	0	0
62	0.099	-0.0578	0.0565	2700041376.0511	1987979708.8747	44586.7661
63	0.0787	-0.0529	0.0553	3590355967.9129	2522105128.5541	50220.5648
64	0.0582	-0.0116	0.0444	316339066.1667	1970663612.9573	44392.1571
65	0.0551	-0.0712	0.0497	13276783805.5145	4231887651.4687	65052.9604
66	0.0581	-0.0179	0.0444	756989276.2136	3652737922.2595	60437.8848
67	0.0297	-0.0441	0.0444	17450198614.7012	5623803735.4655	74992.0245
68	0.0336	0.0505	0.0451	17965314429.7776	7166492572.2545	84655.1391
69	0.0647	0.0099	0.0412	185959766.1334	6390877816.0188	79942.966
70	0.0656	0.006	0.0377	65831852.2171	5758373219.6387	75883.9457
71	0.0927	-0.0155	0.0357	223240214.9774	5255179310.124	72492.6156
72	0.1035	-0.0013	0.0328	1210121.258	4817348544.3852	69407.1217

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 2 ; 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,par1))
(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.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- 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$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
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[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
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:par1] <- 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.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[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