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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 computationMon, 15 Dec 2008 07:52:51 -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/15/t1229352856sybw0k04k9gsipb.htm/, Retrieved Thu, 09 May 2024 14:54:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33705, Retrieved Thu, 09 May 2024 14:54:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsARIMA forecasting- paper
Estimated Impact263

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [Paper - Arima For...] [2008-12-14 14:14:00] [7a664918911e34206ce9d0436dd7c1c8]
-   P     [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-15 14:52:51] [0cdfeda4aa2f9e551c2e529c44a404df] [Current]
-  MPD      [ARIMA Forecasting] [paper: 10 Forecast] [2009-12-11 15:59:42] [0f0e461427f61416e46aeda5f4901bed]
-  M D      [ARIMA Forecasting] [] [2009-12-14 19:07:20] [cf890101a20378422561610e0d41fd9c]
-  M D      [ARIMA Forecasting] [] [2009-12-14 19:07:20] [cf890101a20378422561610e0d41fd9c]
-   P         [ARIMA Forecasting] [] [2009-12-17 10:19:20] [cf890101a20378422561610e0d41fd9c]
- R PD          [ARIMA Forecasting] [] [2010-12-21 14:02:55] [4f85667043e8913570b3eb8f368f82b2]
- R PD          [ARIMA Forecasting] [] [2010-12-21 14:02:55] [4f85667043e8913570b3eb8f368f82b2]
- R  D          [ARIMA Forecasting] [] [2010-12-22 10:55:23] [4f85667043e8913570b3eb8f368f82b2]
-  MPD      [ARIMA Forecasting] [univariate arima ...] [2009-12-15 20:49:36] [ba905ddf7cdf9ecb063c35348c4dab2e]
-   PD        [ARIMA Forecasting] [arima] [2009-12-24 18:21:27] [ba905ddf7cdf9ecb063c35348c4dab2e]
-  MPD      [ARIMA Forecasting] [Paper ARIMA forec...] [2009-12-18 09:44:08] [4395c69e961f9a13a0559fd2f0a72538]
- RMPD      [ARIMA Backward Selection] [] [2009-12-18 12:43:09] [5edbdb7a459c4059b6c3b063ba86821c]
-    D        [ARIMA Backward Selection] [] [2009-12-18 12:47:20] [5edbdb7a459c4059b6c3b063ba86821c]
-  MPD      [ARIMA Forecasting] [paper 10] [2009-12-20 16:27:27] [4a2be4899cba879e4eea9daa25281df8]
-  M D      [ARIMA Forecasting] [ARIMA Forecasting...] [2009-12-20 21:59:01] [73863f7f907331e734eff34b7de6fc83]
-  MPD      [ARIMA Forecasting] [ARIMA Forecasting...] [2009-12-21 11:34:13] [73863f7f907331e734eff34b7de6fc83]
- RMPD      [ARIMA Forecasting] [] [2009-12-21 16:08:37] [5d3787a0898969f50f64a85def6703e1]
- RMPD      [ARIMA Forecasting] [] [2009-12-21 16:27:37] [5d3787a0898969f50f64a85def6703e1]
- RMPD      [ARIMA Forecasting] [] [2009-12-21 16:29:37] [5d3787a0898969f50f64a85def6703e1]
-  MPD      [ARIMA Forecasting] [ARIMA FORECAST JD...] [2009-12-21 17:10:18] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14929387,5
14717825,3
15826281,2
16301309,6
15033016,9
16998460,6
14066462,7
13328937,3
17319718,2
17586426,8
15887037,4
17935679,1
15869489
15892510,9
17556558,1
16791643
15953688,5
18144913,6
14390881
13885708,7
17332571,5
17152595,8
16003877,1
16841467,1
14783398,1
14667847,5
17714362,2
16282088
15014866,2
17722582,4
13876509,4
15495489,6
17799521,1
17920079,1
17248022,4
18813782,4
16249688,3
17823358,5
20424438,3
17814218,7
19699959,6
19776328,1
15679833,1
17119266,5
20092613
20863688,3
20925203,1
21032593
20664684,3
19711511,4
22553293,4
19498332,9
20722827,8
21321275
17960847,7
17789654,9
20003708,5
21169851,7
20422839,4
19810562,3

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33705&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33705&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33705&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'George Udny Yule' @ 72.249.76.132






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[48])
3618813782.4-------
3716249688.3-------
3817823358.5-------
3920424438.3-------
4017814218.7-------
4119699959.6-------
4219776328.1-------
4315679833.1-------
4417119266.5-------
4520092613-------
4620863688.3-------
4720925203.1-------
4821032593-------
4920664684.318912369.07117120337.203520704400.93850.02760.01020.99820.0102
5019711511.420486039.27118494542.738922477535.80310.22290.43020.99560.2953
5122553293.423087119.07120914392.981425259845.16060.31510.99880.99180.9681
5219498332.920476899.47118136938.171422816860.77060.20620.0410.98710.3208
5320722827.822362640.37119866623.723124858657.0190.09890.98780.98170.8519
542132127522439008.87119796135.561525081882.18050.20360.89840.97580.8515
5517960847.718342513.87115560525.453921124502.28820.3940.01790.96970.029
5617789654.919781947.27116867476.516922696418.02510.09020.88970.96330.2002
5720003708.522755293.77119714106.502925796481.03910.03810.99930.95690.8666
5821169851.723526369.07120363538.025526689200.11660.07210.98550.95050.9389
5920422839.423587883.87120307917.339826867850.40220.02930.92580.94420.9366
6019810562.323695273.77120302213.107127088334.43490.01240.97060.9380.938

\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[48]) \tabularnewline
36 & 18813782.4 & - & - & - & - & - & - & - \tabularnewline
37 & 16249688.3 & - & - & - & - & - & - & - \tabularnewline
38 & 17823358.5 & - & - & - & - & - & - & - \tabularnewline
39 & 20424438.3 & - & - & - & - & - & - & - \tabularnewline
40 & 17814218.7 & - & - & - & - & - & - & - \tabularnewline
41 & 19699959.6 & - & - & - & - & - & - & - \tabularnewline
42 & 19776328.1 & - & - & - & - & - & - & - \tabularnewline
43 & 15679833.1 & - & - & - & - & - & - & - \tabularnewline
44 & 17119266.5 & - & - & - & - & - & - & - \tabularnewline
45 & 20092613 & - & - & - & - & - & - & - \tabularnewline
46 & 20863688.3 & - & - & - & - & - & - & - \tabularnewline
47 & 20925203.1 & - & - & - & - & - & - & - \tabularnewline
48 & 21032593 & - & - & - & - & - & - & - \tabularnewline
49 & 20664684.3 & 18912369.071 & 17120337.2035 & 20704400.9385 & 0.0276 & 0.0102 & 0.9982 & 0.0102 \tabularnewline
50 & 19711511.4 & 20486039.271 & 18494542.7389 & 22477535.8031 & 0.2229 & 0.4302 & 0.9956 & 0.2953 \tabularnewline
51 & 22553293.4 & 23087119.071 & 20914392.9814 & 25259845.1606 & 0.3151 & 0.9988 & 0.9918 & 0.9681 \tabularnewline
52 & 19498332.9 & 20476899.471 & 18136938.1714 & 22816860.7706 & 0.2062 & 0.041 & 0.9871 & 0.3208 \tabularnewline
53 & 20722827.8 & 22362640.371 & 19866623.7231 & 24858657.019 & 0.0989 & 0.9878 & 0.9817 & 0.8519 \tabularnewline
54 & 21321275 & 22439008.871 & 19796135.5615 & 25081882.1805 & 0.2036 & 0.8984 & 0.9758 & 0.8515 \tabularnewline
55 & 17960847.7 & 18342513.871 & 15560525.4539 & 21124502.2882 & 0.394 & 0.0179 & 0.9697 & 0.029 \tabularnewline
56 & 17789654.9 & 19781947.271 & 16867476.5169 & 22696418.0251 & 0.0902 & 0.8897 & 0.9633 & 0.2002 \tabularnewline
57 & 20003708.5 & 22755293.771 & 19714106.5029 & 25796481.0391 & 0.0381 & 0.9993 & 0.9569 & 0.8666 \tabularnewline
58 & 21169851.7 & 23526369.071 & 20363538.0255 & 26689200.1166 & 0.0721 & 0.9855 & 0.9505 & 0.9389 \tabularnewline
59 & 20422839.4 & 23587883.871 & 20307917.3398 & 26867850.4022 & 0.0293 & 0.9258 & 0.9442 & 0.9366 \tabularnewline
60 & 19810562.3 & 23695273.771 & 20302213.1071 & 27088334.4349 & 0.0124 & 0.9706 & 0.938 & 0.938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33705&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[48])[/C][/ROW]
[ROW][C]36[/C][C]18813782.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]16249688.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]17823358.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]20424438.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]17814218.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]19699959.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]19776328.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]15679833.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]17119266.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]20092613[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]20863688.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]20925203.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]21032593[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]20664684.3[/C][C]18912369.071[/C][C]17120337.2035[/C][C]20704400.9385[/C][C]0.0276[/C][C]0.0102[/C][C]0.9982[/C][C]0.0102[/C][/ROW]
[ROW][C]50[/C][C]19711511.4[/C][C]20486039.271[/C][C]18494542.7389[/C][C]22477535.8031[/C][C]0.2229[/C][C]0.4302[/C][C]0.9956[/C][C]0.2953[/C][/ROW]
[ROW][C]51[/C][C]22553293.4[/C][C]23087119.071[/C][C]20914392.9814[/C][C]25259845.1606[/C][C]0.3151[/C][C]0.9988[/C][C]0.9918[/C][C]0.9681[/C][/ROW]
[ROW][C]52[/C][C]19498332.9[/C][C]20476899.471[/C][C]18136938.1714[/C][C]22816860.7706[/C][C]0.2062[/C][C]0.041[/C][C]0.9871[/C][C]0.3208[/C][/ROW]
[ROW][C]53[/C][C]20722827.8[/C][C]22362640.371[/C][C]19866623.7231[/C][C]24858657.019[/C][C]0.0989[/C][C]0.9878[/C][C]0.9817[/C][C]0.8519[/C][/ROW]
[ROW][C]54[/C][C]21321275[/C][C]22439008.871[/C][C]19796135.5615[/C][C]25081882.1805[/C][C]0.2036[/C][C]0.8984[/C][C]0.9758[/C][C]0.8515[/C][/ROW]
[ROW][C]55[/C][C]17960847.7[/C][C]18342513.871[/C][C]15560525.4539[/C][C]21124502.2882[/C][C]0.394[/C][C]0.0179[/C][C]0.9697[/C][C]0.029[/C][/ROW]
[ROW][C]56[/C][C]17789654.9[/C][C]19781947.271[/C][C]16867476.5169[/C][C]22696418.0251[/C][C]0.0902[/C][C]0.8897[/C][C]0.9633[/C][C]0.2002[/C][/ROW]
[ROW][C]57[/C][C]20003708.5[/C][C]22755293.771[/C][C]19714106.5029[/C][C]25796481.0391[/C][C]0.0381[/C][C]0.9993[/C][C]0.9569[/C][C]0.8666[/C][/ROW]
[ROW][C]58[/C][C]21169851.7[/C][C]23526369.071[/C][C]20363538.0255[/C][C]26689200.1166[/C][C]0.0721[/C][C]0.9855[/C][C]0.9505[/C][C]0.9389[/C][/ROW]
[ROW][C]59[/C][C]20422839.4[/C][C]23587883.871[/C][C]20307917.3398[/C][C]26867850.4022[/C][C]0.0293[/C][C]0.9258[/C][C]0.9442[/C][C]0.9366[/C][/ROW]
[ROW][C]60[/C][C]19810562.3[/C][C]23695273.771[/C][C]20302213.1071[/C][C]27088334.4349[/C][C]0.0124[/C][C]0.9706[/C][C]0.938[/C][C]0.938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33705&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33705&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[48])
3618813782.4-------
3716249688.3-------
3817823358.5-------
3920424438.3-------
4017814218.7-------
4119699959.6-------
4219776328.1-------
4315679833.1-------
4417119266.5-------
4520092613-------
4620863688.3-------
4720925203.1-------
4821032593-------
4920664684.318912369.07117120337.203520704400.93850.02760.01020.99820.0102
5019711511.420486039.27118494542.738922477535.80310.22290.43020.99560.2953
5122553293.423087119.07120914392.981425259845.16060.31510.99880.99180.9681
5219498332.920476899.47118136938.171422816860.77060.20620.0410.98710.3208
5320722827.822362640.37119866623.723124858657.0190.09890.98780.98170.8519
542132127522439008.87119796135.561525081882.18050.20360.89840.97580.8515
5517960847.718342513.87115560525.453921124502.28820.3940.01790.96970.029
5617789654.919781947.27116867476.516922696418.02510.09020.88970.96330.2002
5720003708.522755293.77119714106.502925796481.03910.03810.99930.95690.8666
5821169851.723526369.07120363538.025526689200.11660.07210.98550.95050.9389
5920422839.423587883.87120307917.339826867850.40220.02930.92580.94420.9366
6019810562.323695273.77120302213.107127088334.43490.01240.97060.9380.938






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.04830.09270.00773070608661745.07255884055145.422505849.8346
500.0496-0.03780.0032599893422973.58349991118581.1319223586.9374
510.048-0.02310.0019284969847030.86623747487252.5722154102.1974
520.0583-0.04780.004957592533901.17379799377825.0978282487.8366
530.0569-0.07330.00612688985268047.28224082105670.607473373.1146
540.0601-0.04980.00421249329006406.31104110750533.859322661.9757
550.0774-0.02080.0017145669066094.56312139088841.2135110177.5333
560.0752-0.10070.00843969228891590.56330769074299.214575125.2684
570.0682-0.12090.01017571221503647.36630935125303.946794314.2485
580.0686-0.10020.00835553174119878.91462764509989.909680267.9693
590.0709-0.13420.011210017506503480.4834792208623.367913669.6387
600.0731-0.16390.013715090983213008.21257581934417.351121419.6068

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0483 & 0.0927 & 0.0077 & 3070608661745.07 & 255884055145.422 & 505849.8346 \tabularnewline
50 & 0.0496 & -0.0378 & 0.0032 & 599893422973.583 & 49991118581.1319 & 223586.9374 \tabularnewline
51 & 0.048 & -0.0231 & 0.0019 & 284969847030.866 & 23747487252.5722 & 154102.1974 \tabularnewline
52 & 0.0583 & -0.0478 & 0.004 & 957592533901.173 & 79799377825.0978 & 282487.8366 \tabularnewline
53 & 0.0569 & -0.0733 & 0.0061 & 2688985268047.28 & 224082105670.607 & 473373.1146 \tabularnewline
54 & 0.0601 & -0.0498 & 0.0042 & 1249329006406.31 & 104110750533.859 & 322661.9757 \tabularnewline
55 & 0.0774 & -0.0208 & 0.0017 & 145669066094.563 & 12139088841.2135 & 110177.5333 \tabularnewline
56 & 0.0752 & -0.1007 & 0.0084 & 3969228891590.56 & 330769074299.214 & 575125.2684 \tabularnewline
57 & 0.0682 & -0.1209 & 0.0101 & 7571221503647.36 & 630935125303.946 & 794314.2485 \tabularnewline
58 & 0.0686 & -0.1002 & 0.0083 & 5553174119878.91 & 462764509989.909 & 680267.9693 \tabularnewline
59 & 0.0709 & -0.1342 & 0.0112 & 10017506503480.4 & 834792208623.367 & 913669.6387 \tabularnewline
60 & 0.0731 & -0.1639 & 0.0137 & 15090983213008.2 & 1257581934417.35 & 1121419.6068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33705&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]49[/C][C]0.0483[/C][C]0.0927[/C][C]0.0077[/C][C]3070608661745.07[/C][C]255884055145.422[/C][C]505849.8346[/C][/ROW]
[ROW][C]50[/C][C]0.0496[/C][C]-0.0378[/C][C]0.0032[/C][C]599893422973.583[/C][C]49991118581.1319[/C][C]223586.9374[/C][/ROW]
[ROW][C]51[/C][C]0.048[/C][C]-0.0231[/C][C]0.0019[/C][C]284969847030.866[/C][C]23747487252.5722[/C][C]154102.1974[/C][/ROW]
[ROW][C]52[/C][C]0.0583[/C][C]-0.0478[/C][C]0.004[/C][C]957592533901.173[/C][C]79799377825.0978[/C][C]282487.8366[/C][/ROW]
[ROW][C]53[/C][C]0.0569[/C][C]-0.0733[/C][C]0.0061[/C][C]2688985268047.28[/C][C]224082105670.607[/C][C]473373.1146[/C][/ROW]
[ROW][C]54[/C][C]0.0601[/C][C]-0.0498[/C][C]0.0042[/C][C]1249329006406.31[/C][C]104110750533.859[/C][C]322661.9757[/C][/ROW]
[ROW][C]55[/C][C]0.0774[/C][C]-0.0208[/C][C]0.0017[/C][C]145669066094.563[/C][C]12139088841.2135[/C][C]110177.5333[/C][/ROW]
[ROW][C]56[/C][C]0.0752[/C][C]-0.1007[/C][C]0.0084[/C][C]3969228891590.56[/C][C]330769074299.214[/C][C]575125.2684[/C][/ROW]
[ROW][C]57[/C][C]0.0682[/C][C]-0.1209[/C][C]0.0101[/C][C]7571221503647.36[/C][C]630935125303.946[/C][C]794314.2485[/C][/ROW]
[ROW][C]58[/C][C]0.0686[/C][C]-0.1002[/C][C]0.0083[/C][C]5553174119878.91[/C][C]462764509989.909[/C][C]680267.9693[/C][/ROW]
[ROW][C]59[/C][C]0.0709[/C][C]-0.1342[/C][C]0.0112[/C][C]10017506503480.4[/C][C]834792208623.367[/C][C]913669.6387[/C][/ROW]
[ROW][C]60[/C][C]0.0731[/C][C]-0.1639[/C][C]0.0137[/C][C]15090983213008.2[/C][C]1257581934417.35[/C][C]1121419.6068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33705&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33705&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
490.04830.09270.00773070608661745.07255884055145.422505849.8346
500.0496-0.03780.0032599893422973.58349991118581.1319223586.9374
510.048-0.02310.0019284969847030.86623747487252.5722154102.1974
520.0583-0.04780.004957592533901.17379799377825.0978282487.8366
530.0569-0.07330.00612688985268047.28224082105670.607473373.1146
540.0601-0.04980.00421249329006406.31104110750533.859322661.9757
550.0774-0.02080.0017145669066094.56312139088841.2135110177.5333
560.0752-0.10070.00843969228891590.56330769074299.214575125.2684
570.0682-0.12090.01017571221503647.36630935125303.946794314.2485
580.0686-0.10020.00835553174119878.91462764509989.909680267.9693
590.0709-0.13420.011210017506503480.4834792208623.367913669.6387
600.0731-0.16390.013715090983213008.21257581934417.351121419.6068


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; 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')