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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, 21 Dec 2008 06:12:31 -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/21/t122986521294jc5mpoifvjge0.htm/, Retrieved Sun, 26 May 2024 03:40:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35555, Retrieved Sun, 26 May 2024 03:40:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact213

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Import uit Amerika] [2008-10-13 18:55:55] [b943bd7078334192ff8343563ee31113]
- RMPD  [Histogram] [Paper Analyse (1)] [2008-12-13 13:37:46] [b943bd7078334192ff8343563ee31113]
- RMP     [Tukey lambda PPCC Plot] [Paper Analyse (2)] [2008-12-13 14:19:33] [b943bd7078334192ff8343563ee31113]
- RM        [Central Tendency] [Paper Analyse (3)] [2008-12-13 14:48:04] [b943bd7078334192ff8343563ee31113]
- RMP         [Mean Plot] [Paper Analyse (4)] [2008-12-13 16:59:19] [b943bd7078334192ff8343563ee31113]
- RMPD          [Pearson Correlation] [Paper Analyse (5)] [2008-12-13 17:21:52] [b943bd7078334192ff8343563ee31113]
-    D            [Pearson Correlation] [Paper Analyse (6)] [2008-12-13 17:43:27] [b943bd7078334192ff8343563ee31113]
- RM D              [Partial Correlation] [Paper Analyse (7)] [2008-12-13 19:17:34] [b943bd7078334192ff8343563ee31113]
- RMPD                [Standard Deviation-Mean Plot] [Paper Analyse (8)] [2008-12-13 20:10:46] [b943bd7078334192ff8343563ee31113]
- RM                    [Variance Reduction Matrix] [Paper Analyse (9)] [2008-12-13 20:12:45] [b943bd7078334192ff8343563ee31113]
- RMP                     [(Partial) Autocorrelation Function] [Paper Analyse (10)] [2008-12-14 09:58:13] [b943bd7078334192ff8343563ee31113]
-   P                       [(Partial) Autocorrelation Function] [Paper Analyse (16)] [2008-12-21 11:54:36] [b943bd7078334192ff8343563ee31113]
-   P                         [(Partial) Autocorrelation Function] [Paper Analyse (17)] [2008-12-21 11:57:49] [b943bd7078334192ff8343563ee31113]
- RMP                           [Spectral Analysis] [Paper Analyse (18)] [2008-12-21 12:02:44] [b943bd7078334192ff8343563ee31113]
-   P                             [Spectral Analysis] [Paper Analyse (19)] [2008-12-21 12:06:49] [b943bd7078334192ff8343563ee31113]
- RMP                               [ARIMA Backward Selection] [Paper Analyse (20)] [2008-12-21 12:13:35] [b943bd7078334192ff8343563ee31113]
- RMP                                   [ARIMA Forecasting] [Paper Analyse (21)] [2008-12-21 13:12:31] [620b6ad5c4696049e39cb73ce029682c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1593
1477.9
1733.7
1569.7
1843.7
1950.3
1657.5
1772.1
1568.3
1809.8
1646.7
1808.5
1763.9
1625.5
1538.8
1342.4
1645.1
1619.9
1338.1
1505.5
1529.1
1511.9
1656.7
1694.4
1662.3
1588.7
1483.3
1585.6
1658.9
1584.4
1470.6
1618.7
1407.6
1473.9
1515.3
1485.4
1496.1
1493.5
1298.4
1375.3
1507.9
1455.3
1363.3
1392.8
1348.8
1880.3
1669.2
1543.6
1701.2
1516.5
1466.8
1484.1
1577.2
1684.5
1414.7
1674.5
1598.7
1739.1
1674.6
1671.8
1802
1526.8
1580.9
1634.8
1610.3
1712
1678.8
1708.1
1680.6
2056
1624
2021.4
1861.1
1750.8
1767.5
1710.3
2151.5
2047.9
1915.4
1984.7
1896.5
2170.8
2139.9
2330.5
2121.8
2226.8
1857.9
2155.9
2341.7
2290.2
2006.5
2111.9
1731.3
1762.2
1863.2
1943.5
1975.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35555&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35555&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






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[85])
731861.1-------
741750.8-------
751767.5-------
761710.3-------
772151.5-------
782047.9-------
791915.4-------
801984.7-------
811896.5-------
822170.8-------
832139.9-------
842330.5-------
852121.8-------
862226.82010.13431715.00292436.87890.15980.3040.88320.304
871857.91974.16641673.4682416.34570.30320.13140.82020.2564
882155.91948.99761641.45912409.02390.1890.6510.84540.2308
892341.72187.42011787.99292835.47050.32040.5380.54330.5787
902290.22199.85181780.9212898.21960.39990.34530.66510.5867
912006.51959.2371610.99532515.02630.43380.12160.56140.2832
922111.92125.36131706.50372840.25830.48530.62770.65010.5039
931731.32004.92461618.57272654.14180.20440.37340.62830.3621
941762.22304.20931790.26363271.68540.13610.87710.60650.6441
951863.22181.39111705.50853060.17510.2390.82510.53690.5529
961943.52279.02431751.33413307.00870.26120.78610.46090.6178
971975.22260.8021729.3293311.42130.29710.72310.60230.6023

\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[85]) \tabularnewline
73 & 1861.1 & - & - & - & - & - & - & - \tabularnewline
74 & 1750.8 & - & - & - & - & - & - & - \tabularnewline
75 & 1767.5 & - & - & - & - & - & - & - \tabularnewline
76 & 1710.3 & - & - & - & - & - & - & - \tabularnewline
77 & 2151.5 & - & - & - & - & - & - & - \tabularnewline
78 & 2047.9 & - & - & - & - & - & - & - \tabularnewline
79 & 1915.4 & - & - & - & - & - & - & - \tabularnewline
80 & 1984.7 & - & - & - & - & - & - & - \tabularnewline
81 & 1896.5 & - & - & - & - & - & - & - \tabularnewline
82 & 2170.8 & - & - & - & - & - & - & - \tabularnewline
83 & 2139.9 & - & - & - & - & - & - & - \tabularnewline
84 & 2330.5 & - & - & - & - & - & - & - \tabularnewline
85 & 2121.8 & - & - & - & - & - & - & - \tabularnewline
86 & 2226.8 & 2010.1343 & 1715.0029 & 2436.8789 & 0.1598 & 0.304 & 0.8832 & 0.304 \tabularnewline
87 & 1857.9 & 1974.1664 & 1673.468 & 2416.3457 & 0.3032 & 0.1314 & 0.8202 & 0.2564 \tabularnewline
88 & 2155.9 & 1948.9976 & 1641.4591 & 2409.0239 & 0.189 & 0.651 & 0.8454 & 0.2308 \tabularnewline
89 & 2341.7 & 2187.4201 & 1787.9929 & 2835.4705 & 0.3204 & 0.538 & 0.5433 & 0.5787 \tabularnewline
90 & 2290.2 & 2199.8518 & 1780.921 & 2898.2196 & 0.3999 & 0.3453 & 0.6651 & 0.5867 \tabularnewline
91 & 2006.5 & 1959.237 & 1610.9953 & 2515.0263 & 0.4338 & 0.1216 & 0.5614 & 0.2832 \tabularnewline
92 & 2111.9 & 2125.3613 & 1706.5037 & 2840.2583 & 0.4853 & 0.6277 & 0.6501 & 0.5039 \tabularnewline
93 & 1731.3 & 2004.9246 & 1618.5727 & 2654.1418 & 0.2044 & 0.3734 & 0.6283 & 0.3621 \tabularnewline
94 & 1762.2 & 2304.2093 & 1790.2636 & 3271.6854 & 0.1361 & 0.8771 & 0.6065 & 0.6441 \tabularnewline
95 & 1863.2 & 2181.3911 & 1705.5085 & 3060.1751 & 0.239 & 0.8251 & 0.5369 & 0.5529 \tabularnewline
96 & 1943.5 & 2279.0243 & 1751.3341 & 3307.0087 & 0.2612 & 0.7861 & 0.4609 & 0.6178 \tabularnewline
97 & 1975.2 & 2260.802 & 1729.329 & 3311.4213 & 0.2971 & 0.7231 & 0.6023 & 0.6023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35555&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[85])[/C][/ROW]
[ROW][C]73[/C][C]1861.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]74[/C][C]1750.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]75[/C][C]1767.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]76[/C][C]1710.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]77[/C][C]2151.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]78[/C][C]2047.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]79[/C][C]1915.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]80[/C][C]1984.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]81[/C][C]1896.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]2170.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]2139.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]2330.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]2121.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]2226.8[/C][C]2010.1343[/C][C]1715.0029[/C][C]2436.8789[/C][C]0.1598[/C][C]0.304[/C][C]0.8832[/C][C]0.304[/C][/ROW]
[ROW][C]87[/C][C]1857.9[/C][C]1974.1664[/C][C]1673.468[/C][C]2416.3457[/C][C]0.3032[/C][C]0.1314[/C][C]0.8202[/C][C]0.2564[/C][/ROW]
[ROW][C]88[/C][C]2155.9[/C][C]1948.9976[/C][C]1641.4591[/C][C]2409.0239[/C][C]0.189[/C][C]0.651[/C][C]0.8454[/C][C]0.2308[/C][/ROW]
[ROW][C]89[/C][C]2341.7[/C][C]2187.4201[/C][C]1787.9929[/C][C]2835.4705[/C][C]0.3204[/C][C]0.538[/C][C]0.5433[/C][C]0.5787[/C][/ROW]
[ROW][C]90[/C][C]2290.2[/C][C]2199.8518[/C][C]1780.921[/C][C]2898.2196[/C][C]0.3999[/C][C]0.3453[/C][C]0.6651[/C][C]0.5867[/C][/ROW]
[ROW][C]91[/C][C]2006.5[/C][C]1959.237[/C][C]1610.9953[/C][C]2515.0263[/C][C]0.4338[/C][C]0.1216[/C][C]0.5614[/C][C]0.2832[/C][/ROW]
[ROW][C]92[/C][C]2111.9[/C][C]2125.3613[/C][C]1706.5037[/C][C]2840.2583[/C][C]0.4853[/C][C]0.6277[/C][C]0.6501[/C][C]0.5039[/C][/ROW]
[ROW][C]93[/C][C]1731.3[/C][C]2004.9246[/C][C]1618.5727[/C][C]2654.1418[/C][C]0.2044[/C][C]0.3734[/C][C]0.6283[/C][C]0.3621[/C][/ROW]
[ROW][C]94[/C][C]1762.2[/C][C]2304.2093[/C][C]1790.2636[/C][C]3271.6854[/C][C]0.1361[/C][C]0.8771[/C][C]0.6065[/C][C]0.6441[/C][/ROW]
[ROW][C]95[/C][C]1863.2[/C][C]2181.3911[/C][C]1705.5085[/C][C]3060.1751[/C][C]0.239[/C][C]0.8251[/C][C]0.5369[/C][C]0.5529[/C][/ROW]
[ROW][C]96[/C][C]1943.5[/C][C]2279.0243[/C][C]1751.3341[/C][C]3307.0087[/C][C]0.2612[/C][C]0.7861[/C][C]0.4609[/C][C]0.6178[/C][/ROW]
[ROW][C]97[/C][C]1975.2[/C][C]2260.802[/C][C]1729.329[/C][C]3311.4213[/C][C]0.2971[/C][C]0.7231[/C][C]0.6023[/C][C]0.6023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35555&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[85])
731861.1-------
741750.8-------
751767.5-------
761710.3-------
772151.5-------
782047.9-------
791915.4-------
801984.7-------
811896.5-------
822170.8-------
832139.9-------
842330.5-------
852121.8-------
862226.82010.13431715.00292436.87890.15980.3040.88320.304
871857.91974.16641673.4682416.34570.30320.13140.82020.2564
882155.91948.99761641.45912409.02390.1890.6510.84540.2308
892341.72187.42011787.99292835.47050.32040.5380.54330.5787
902290.22199.85181780.9212898.21960.39990.34530.66510.5867
912006.51959.2371610.99532515.02630.43380.12160.56140.2832
922111.92125.36131706.50372840.25830.48530.62770.65010.5039
931731.32004.92461618.57272654.14180.20440.37340.62830.3621
941762.22304.20931790.26363271.68540.13610.87710.60650.6441
951863.22181.39111705.50853060.17510.2390.82510.53690.5529
961943.52279.02431751.33413307.00870.26120.78610.46090.6178
971975.22260.8021729.3293311.42130.29710.72310.60230.6023






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
860.10830.10780.00946944.01073912.000962.546
870.1143-0.05890.004913517.87421126.489533.5632
880.12040.10620.008842808.58473567.382159.7276
890.15120.07050.005923802.29211983.524344.5368
900.1620.04110.00348162.7949680.232926.0813
910.14470.02410.0022233.788186.14913.6436
920.1716-0.00635e-04181.207415.10063.886
930.1652-0.13650.011474870.4316239.202678.9886
940.2142-0.23520.0196293774.052524481.171156.4646
950.2055-0.14590.0122101245.5788437.131591.8539
960.2301-0.14720.0123112576.53839381.378296.8575
970.2371-0.12630.010581568.49616797.374782.4462

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
86 & 0.1083 & 0.1078 & 0.009 & 46944.0107 & 3912.0009 & 62.546 \tabularnewline
87 & 0.1143 & -0.0589 & 0.0049 & 13517.8742 & 1126.4895 & 33.5632 \tabularnewline
88 & 0.1204 & 0.1062 & 0.0088 & 42808.5847 & 3567.3821 & 59.7276 \tabularnewline
89 & 0.1512 & 0.0705 & 0.0059 & 23802.2921 & 1983.5243 & 44.5368 \tabularnewline
90 & 0.162 & 0.0411 & 0.0034 & 8162.7949 & 680.2329 & 26.0813 \tabularnewline
91 & 0.1447 & 0.0241 & 0.002 & 2233.788 & 186.149 & 13.6436 \tabularnewline
92 & 0.1716 & -0.0063 & 5e-04 & 181.2074 & 15.1006 & 3.886 \tabularnewline
93 & 0.1652 & -0.1365 & 0.0114 & 74870.431 & 6239.2026 & 78.9886 \tabularnewline
94 & 0.2142 & -0.2352 & 0.0196 & 293774.0525 & 24481.171 & 156.4646 \tabularnewline
95 & 0.2055 & -0.1459 & 0.0122 & 101245.578 & 8437.1315 & 91.8539 \tabularnewline
96 & 0.2301 & -0.1472 & 0.0123 & 112576.5383 & 9381.3782 & 96.8575 \tabularnewline
97 & 0.2371 & -0.1263 & 0.0105 & 81568.4961 & 6797.3747 & 82.4462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35555&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]86[/C][C]0.1083[/C][C]0.1078[/C][C]0.009[/C][C]46944.0107[/C][C]3912.0009[/C][C]62.546[/C][/ROW]
[ROW][C]87[/C][C]0.1143[/C][C]-0.0589[/C][C]0.0049[/C][C]13517.8742[/C][C]1126.4895[/C][C]33.5632[/C][/ROW]
[ROW][C]88[/C][C]0.1204[/C][C]0.1062[/C][C]0.0088[/C][C]42808.5847[/C][C]3567.3821[/C][C]59.7276[/C][/ROW]
[ROW][C]89[/C][C]0.1512[/C][C]0.0705[/C][C]0.0059[/C][C]23802.2921[/C][C]1983.5243[/C][C]44.5368[/C][/ROW]
[ROW][C]90[/C][C]0.162[/C][C]0.0411[/C][C]0.0034[/C][C]8162.7949[/C][C]680.2329[/C][C]26.0813[/C][/ROW]
[ROW][C]91[/C][C]0.1447[/C][C]0.0241[/C][C]0.002[/C][C]2233.788[/C][C]186.149[/C][C]13.6436[/C][/ROW]
[ROW][C]92[/C][C]0.1716[/C][C]-0.0063[/C][C]5e-04[/C][C]181.2074[/C][C]15.1006[/C][C]3.886[/C][/ROW]
[ROW][C]93[/C][C]0.1652[/C][C]-0.1365[/C][C]0.0114[/C][C]74870.431[/C][C]6239.2026[/C][C]78.9886[/C][/ROW]
[ROW][C]94[/C][C]0.2142[/C][C]-0.2352[/C][C]0.0196[/C][C]293774.0525[/C][C]24481.171[/C][C]156.4646[/C][/ROW]
[ROW][C]95[/C][C]0.2055[/C][C]-0.1459[/C][C]0.0122[/C][C]101245.578[/C][C]8437.1315[/C][C]91.8539[/C][/ROW]
[ROW][C]96[/C][C]0.2301[/C][C]-0.1472[/C][C]0.0123[/C][C]112576.5383[/C][C]9381.3782[/C][C]96.8575[/C][/ROW]
[ROW][C]97[/C][C]0.2371[/C][C]-0.1263[/C][C]0.0105[/C][C]81568.4961[/C][C]6797.3747[/C][C]82.4462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35555&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
860.10830.10780.00946944.01073912.000962.546
870.1143-0.05890.004913517.87421126.489533.5632
880.12040.10620.008842808.58473567.382159.7276
890.15120.07050.005923802.29211983.524344.5368
900.1620.04110.00348162.7949680.232926.0813
910.14470.02410.0022233.788186.14913.6436
920.1716-0.00635e-04181.207415.10063.886
930.1652-0.13650.011474870.4316239.202678.9886
940.2142-0.23520.0196293774.052524481.171156.4646
950.2055-0.14590.0122101245.5788437.131591.8539
960.2301-0.14720.0123112576.53839381.378296.8575
970.2371-0.12630.010581568.49616797.374782.4462


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = -1.1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = -1.1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 1 ; 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')