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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationSun, 14 Dec 2008 15:42:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/14/t1229294645vd0d88qrwft9ecn.htm/, Retrieved Mon, 13 May 2024 23:29:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33586, Retrieved Mon, 13 May 2024 23:29:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central tendency:...] [2008-12-12 12:54:43] [73d6180dc45497329efd1b6934a84aba]
- RMP   [ARIMA Backward Selection] [ARIMA goudprijs] [2008-12-14 20:12:57] [73d6180dc45497329efd1b6934a84aba]
- RMPD      [ARIMA Forecasting] [ARIMA forecast: O...] [2008-12-14 22:42:36] [e81ac192d6ae6d77191d83851a692999] [Current]
-   PD        [ARIMA Forecasting] [arima forecast ol...] [2008-12-16 16:27:50] [73d6180dc45497329efd1b6934a84aba]
-   P           [ARIMA Forecasting] [Lambda -0,2 ARIMA...] [2008-12-19 21:26:09] [73d6180dc45497329efd1b6934a84aba]
- R  D            [ARIMA Forecasting] [ARIMA Forecast olie] [2008-12-22 13:09:43] [7458e879e85b911182071700fff19fbd]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 22:22:39] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:35:36] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:39:14] [74be16979710d4c4e7c6647856088456]
- R PD            [ARIMA Forecasting] [Forecast BEL20] [2008-12-22 14:06:40] [7458e879e85b911182071700fff19fbd]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
32,68
31,54
32,43
26,54
25,85
27,6
25,71
25,38
28,57
27,64
25,36
25,9
26,29
21,74
19,2
19,32
19,82
20,36
24,31
25,97
25,61
24,67
25,59
26,09
28,37
27,34
24,46
27,46
30,23
32,33
29,87
24,87
25,48
27,28
28,24
29,58
26,95
29,08
28,76
29,59
30,7
30,52
32,67
33,19
37,13
35,54
37,75
41,84
42,94
49,14
44,61
40,22
44,23
45,85
53,38
53,26
51,8
55,3
57,81
63,96
63,77
59,15
56,12
57,42
63,52
61,71
63,01
68,18
72,03
69,75
74,41
74,33
64,24
60,03
59,44
62,5
55,04
58,34
61,92
67,65
67,68
70,3
75,26
71,44
76,36
81,71
92,6
90,6
92,23
94,09
102,79
109,65
124,05
132,69
135,81
116,07
101,42
75,73
55,48

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=33586&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=33586&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33586&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[87])
7559.44-------
7662.5-------
7755.04-------
7858.34-------
7961.92-------
8067.65-------
8167.68-------
8270.3-------
8375.26-------
8471.44-------
8576.36-------
8681.71-------
8792.6-------
8890.6101.378393.2505109.5060.00470.982910.9829
8992.23110.961595.4961126.42680.00880.995110.99
9094.09120.237995.4529145.02280.01930.986610.9856
91102.79129.631294.3363164.92610.0680.97580.99990.9801
92109.65138.9891.9642185.99570.11070.93430.99850.9734
93124.05148.345788.5621208.12930.21290.89770.99590.9662
94132.69157.70584.1692231.24080.25250.81510.99010.9587
95135.81167.066778.8667255.26680.24370.77750.97930.951
96116.07176.427572.7024280.15270.1270.77860.97640.9434
97101.42185.788765.7238305.85360.08420.87250.9630.9359
9875.73195.149757.9688332.33070.0440.90970.94750.9286
9955.48204.510849.4714359.55020.02980.94820.92140.9214

\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[87]) \tabularnewline
75 & 59.44 & - & - & - & - & - & - & - \tabularnewline
76 & 62.5 & - & - & - & - & - & - & - \tabularnewline
77 & 55.04 & - & - & - & - & - & - & - \tabularnewline
78 & 58.34 & - & - & - & - & - & - & - \tabularnewline
79 & 61.92 & - & - & - & - & - & - & - \tabularnewline
80 & 67.65 & - & - & - & - & - & - & - \tabularnewline
81 & 67.68 & - & - & - & - & - & - & - \tabularnewline
82 & 70.3 & - & - & - & - & - & - & - \tabularnewline
83 & 75.26 & - & - & - & - & - & - & - \tabularnewline
84 & 71.44 & - & - & - & - & - & - & - \tabularnewline
85 & 76.36 & - & - & - & - & - & - & - \tabularnewline
86 & 81.71 & - & - & - & - & - & - & - \tabularnewline
87 & 92.6 & - & - & - & - & - & - & - \tabularnewline
88 & 90.6 & 101.3783 & 93.2505 & 109.506 & 0.0047 & 0.9829 & 1 & 0.9829 \tabularnewline
89 & 92.23 & 110.9615 & 95.4961 & 126.4268 & 0.0088 & 0.9951 & 1 & 0.99 \tabularnewline
90 & 94.09 & 120.2379 & 95.4529 & 145.0228 & 0.0193 & 0.9866 & 1 & 0.9856 \tabularnewline
91 & 102.79 & 129.6312 & 94.3363 & 164.9261 & 0.068 & 0.9758 & 0.9999 & 0.9801 \tabularnewline
92 & 109.65 & 138.98 & 91.9642 & 185.9957 & 0.1107 & 0.9343 & 0.9985 & 0.9734 \tabularnewline
93 & 124.05 & 148.3457 & 88.5621 & 208.1293 & 0.2129 & 0.8977 & 0.9959 & 0.9662 \tabularnewline
94 & 132.69 & 157.705 & 84.1692 & 231.2408 & 0.2525 & 0.8151 & 0.9901 & 0.9587 \tabularnewline
95 & 135.81 & 167.0667 & 78.8667 & 255.2668 & 0.2437 & 0.7775 & 0.9793 & 0.951 \tabularnewline
96 & 116.07 & 176.4275 & 72.7024 & 280.1527 & 0.127 & 0.7786 & 0.9764 & 0.9434 \tabularnewline
97 & 101.42 & 185.7887 & 65.7238 & 305.8536 & 0.0842 & 0.8725 & 0.963 & 0.9359 \tabularnewline
98 & 75.73 & 195.1497 & 57.9688 & 332.3307 & 0.044 & 0.9097 & 0.9475 & 0.9286 \tabularnewline
99 & 55.48 & 204.5108 & 49.4714 & 359.5502 & 0.0298 & 0.9482 & 0.9214 & 0.9214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33586&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[87])[/C][/ROW]
[ROW][C]75[/C][C]59.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]76[/C][C]62.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]77[/C][C]55.04[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]78[/C][C]58.34[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]79[/C][C]61.92[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]80[/C][C]67.65[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]81[/C][C]67.68[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]70.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]75.26[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]71.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]76.36[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]81.71[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]87[/C][C]92.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]88[/C][C]90.6[/C][C]101.3783[/C][C]93.2505[/C][C]109.506[/C][C]0.0047[/C][C]0.9829[/C][C]1[/C][C]0.9829[/C][/ROW]
[ROW][C]89[/C][C]92.23[/C][C]110.9615[/C][C]95.4961[/C][C]126.4268[/C][C]0.0088[/C][C]0.9951[/C][C]1[/C][C]0.99[/C][/ROW]
[ROW][C]90[/C][C]94.09[/C][C]120.2379[/C][C]95.4529[/C][C]145.0228[/C][C]0.0193[/C][C]0.9866[/C][C]1[/C][C]0.9856[/C][/ROW]
[ROW][C]91[/C][C]102.79[/C][C]129.6312[/C][C]94.3363[/C][C]164.9261[/C][C]0.068[/C][C]0.9758[/C][C]0.9999[/C][C]0.9801[/C][/ROW]
[ROW][C]92[/C][C]109.65[/C][C]138.98[/C][C]91.9642[/C][C]185.9957[/C][C]0.1107[/C][C]0.9343[/C][C]0.9985[/C][C]0.9734[/C][/ROW]
[ROW][C]93[/C][C]124.05[/C][C]148.3457[/C][C]88.5621[/C][C]208.1293[/C][C]0.2129[/C][C]0.8977[/C][C]0.9959[/C][C]0.9662[/C][/ROW]
[ROW][C]94[/C][C]132.69[/C][C]157.705[/C][C]84.1692[/C][C]231.2408[/C][C]0.2525[/C][C]0.8151[/C][C]0.9901[/C][C]0.9587[/C][/ROW]
[ROW][C]95[/C][C]135.81[/C][C]167.0667[/C][C]78.8667[/C][C]255.2668[/C][C]0.2437[/C][C]0.7775[/C][C]0.9793[/C][C]0.951[/C][/ROW]
[ROW][C]96[/C][C]116.07[/C][C]176.4275[/C][C]72.7024[/C][C]280.1527[/C][C]0.127[/C][C]0.7786[/C][C]0.9764[/C][C]0.9434[/C][/ROW]
[ROW][C]97[/C][C]101.42[/C][C]185.7887[/C][C]65.7238[/C][C]305.8536[/C][C]0.0842[/C][C]0.8725[/C][C]0.963[/C][C]0.9359[/C][/ROW]
[ROW][C]98[/C][C]75.73[/C][C]195.1497[/C][C]57.9688[/C][C]332.3307[/C][C]0.044[/C][C]0.9097[/C][C]0.9475[/C][C]0.9286[/C][/ROW]
[ROW][C]99[/C][C]55.48[/C][C]204.5108[/C][C]49.4714[/C][C]359.5502[/C][C]0.0298[/C][C]0.9482[/C][C]0.9214[/C][C]0.9214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33586&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33586&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[87])
7559.44-------
7662.5-------
7755.04-------
7858.34-------
7961.92-------
8067.65-------
8167.68-------
8270.3-------
8375.26-------
8471.44-------
8576.36-------
8681.71-------
8792.6-------
8890.6101.378393.2505109.5060.00470.982910.9829
8992.23110.961595.4961126.42680.00880.995110.99
9094.09120.237995.4529145.02280.01930.986610.9856
91102.79129.631294.3363164.92610.0680.97580.99990.9801
92109.65138.9891.9642185.99570.11070.93430.99850.9734
93124.05148.345788.5621208.12930.21290.89770.99590.9662
94132.69157.70584.1692231.24080.25250.81510.99010.9587
95135.81167.066778.8667255.26680.24370.77750.97930.951
96116.07176.427572.7024280.15270.1270.77860.97640.9434
97101.42185.788765.7238305.85360.08420.87250.9630.9359
9875.73195.149757.9688332.33070.0440.90970.94750.9286
9955.48204.510849.4714359.55020.02980.94820.92140.9214






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
880.0409-0.10630.0089116.17099.68093.1114
890.0711-0.16880.0141350.868229.2395.4073
900.1052-0.21750.0181683.710656.97597.5482
910.1389-0.20710.0173720.4560.03757.7484
920.1726-0.2110.0176860.246571.68728.4668
930.2056-0.16380.0136590.281649.19017.0136
940.2379-0.15860.0132625.749652.14587.2212
950.2694-0.18710.0156976.983281.41539.023
960.3-0.34210.02853643.0319303.58617.4237
970.3297-0.45410.03787118.0768593.173124.3551
980.3586-0.61190.05114261.06961188.422534.4735
990.3868-0.72870.060722210.17861850.848243.0215

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
88 & 0.0409 & -0.1063 & 0.0089 & 116.1709 & 9.6809 & 3.1114 \tabularnewline
89 & 0.0711 & -0.1688 & 0.0141 & 350.8682 & 29.239 & 5.4073 \tabularnewline
90 & 0.1052 & -0.2175 & 0.0181 & 683.7106 & 56.9759 & 7.5482 \tabularnewline
91 & 0.1389 & -0.2071 & 0.0173 & 720.45 & 60.0375 & 7.7484 \tabularnewline
92 & 0.1726 & -0.211 & 0.0176 & 860.2465 & 71.6872 & 8.4668 \tabularnewline
93 & 0.2056 & -0.1638 & 0.0136 & 590.2816 & 49.1901 & 7.0136 \tabularnewline
94 & 0.2379 & -0.1586 & 0.0132 & 625.7496 & 52.1458 & 7.2212 \tabularnewline
95 & 0.2694 & -0.1871 & 0.0156 & 976.9832 & 81.4153 & 9.023 \tabularnewline
96 & 0.3 & -0.3421 & 0.0285 & 3643.0319 & 303.586 & 17.4237 \tabularnewline
97 & 0.3297 & -0.4541 & 0.0378 & 7118.0768 & 593.1731 & 24.3551 \tabularnewline
98 & 0.3586 & -0.6119 & 0.051 & 14261.0696 & 1188.4225 & 34.4735 \tabularnewline
99 & 0.3868 & -0.7287 & 0.0607 & 22210.1786 & 1850.8482 & 43.0215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33586&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]88[/C][C]0.0409[/C][C]-0.1063[/C][C]0.0089[/C][C]116.1709[/C][C]9.6809[/C][C]3.1114[/C][/ROW]
[ROW][C]89[/C][C]0.0711[/C][C]-0.1688[/C][C]0.0141[/C][C]350.8682[/C][C]29.239[/C][C]5.4073[/C][/ROW]
[ROW][C]90[/C][C]0.1052[/C][C]-0.2175[/C][C]0.0181[/C][C]683.7106[/C][C]56.9759[/C][C]7.5482[/C][/ROW]
[ROW][C]91[/C][C]0.1389[/C][C]-0.2071[/C][C]0.0173[/C][C]720.45[/C][C]60.0375[/C][C]7.7484[/C][/ROW]
[ROW][C]92[/C][C]0.1726[/C][C]-0.211[/C][C]0.0176[/C][C]860.2465[/C][C]71.6872[/C][C]8.4668[/C][/ROW]
[ROW][C]93[/C][C]0.2056[/C][C]-0.1638[/C][C]0.0136[/C][C]590.2816[/C][C]49.1901[/C][C]7.0136[/C][/ROW]
[ROW][C]94[/C][C]0.2379[/C][C]-0.1586[/C][C]0.0132[/C][C]625.7496[/C][C]52.1458[/C][C]7.2212[/C][/ROW]
[ROW][C]95[/C][C]0.2694[/C][C]-0.1871[/C][C]0.0156[/C][C]976.9832[/C][C]81.4153[/C][C]9.023[/C][/ROW]
[ROW][C]96[/C][C]0.3[/C][C]-0.3421[/C][C]0.0285[/C][C]3643.0319[/C][C]303.586[/C][C]17.4237[/C][/ROW]
[ROW][C]97[/C][C]0.3297[/C][C]-0.4541[/C][C]0.0378[/C][C]7118.0768[/C][C]593.1731[/C][C]24.3551[/C][/ROW]
[ROW][C]98[/C][C]0.3586[/C][C]-0.6119[/C][C]0.051[/C][C]14261.0696[/C][C]1188.4225[/C][C]34.4735[/C][/ROW]
[ROW][C]99[/C][C]0.3868[/C][C]-0.7287[/C][C]0.0607[/C][C]22210.1786[/C][C]1850.8482[/C][C]43.0215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33586&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33586&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
880.0409-0.10630.0089116.17099.68093.1114
890.0711-0.16880.0141350.868229.2395.4073
900.1052-0.21750.0181683.710656.97597.5482
910.1389-0.20710.0173720.4560.03757.7484
920.1726-0.2110.0176860.246571.68728.4668
930.2056-0.16380.0136590.281649.19017.0136
940.2379-0.15860.0132625.749652.14587.2212
950.2694-0.18710.0156976.983281.41539.023
960.3-0.34210.02853643.0319303.58617.4237
970.3297-0.45410.03787118.0768593.173124.3551
980.3586-0.61190.05114261.06961188.422534.4735
990.3868-0.72870.060722210.17861850.848243.0215


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; 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')