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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 computationFri, 24 Dec 2010 09:42:48 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293183679tfuf4zh4nzll2u0.htm/, Retrieved Tue, 30 Apr 2024 00:49:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114669, Retrieved Tue, 30 Apr 2024 00:49:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
-   PD      [ARIMA Forecasting] [ARIMA forecast ol...] [2010-12-22 22:41:36] [a8a0ff0853b70f438be515083758c362]
-   P           [ARIMA Forecasting] [Arima Forecast ol...] [2010-12-24 09:42:48] [8f110cf3e3846d42560df9b5835185a6] [Current]
-   P             [ARIMA Forecasting] [ARIMA forecasting...] [2010-12-24 21:10:37] [a8a0ff0853b70f438be515083758c362]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
78.33
78.21
78.94
77.94
77.31
75.75
77.73
77.90
77.45
77.46
77.97
77.23
76.56
76.70
76.51
76.03
76.69
76.38
76.80
76.63
77.17
78.63
78.89
76.94
77.50
79.27
79.77
78.62
78.60
77.88
78.71
79.27
80.12
81.12
81.48
82.81
82.39
82.41
82.20
81.99
81.61
83.51
84.05
82.99
83.54
84.44
84.24
83.88
84.17
84.59
84.76
85.14
85.22
84.77
84.50
84.56
83.79
83.96
84.80
84.89
84.78
84.80
84.44
84.65
84.22
84.08
85.29
85.00
84.63
84.92
84.61
84.50
84.29
84.50
84.41
84.71
84.21
83.86
84.40
83.71
84.42
85.26
85.08
85.65
85.74
85.89
86.08
85.49
85.97
85.84
86.72
85.42
83.87
85.45
85.35
84.27
83.13
83.79
83.70
83.76
83.47
83.78
84.83
84.43
84.90
85.36
85.49
85.29

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114669&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]2 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=114669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114669&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 time2 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[96])
8485.65-------
8585.74-------
8685.89-------
8786.08-------
8885.49-------
8985.97-------
9085.84-------
9186.72-------
9285.42-------
9383.87-------
9485.45-------
9585.35-------
9684.27-------
9783.1384.416283.075185.75720.03010.58460.02650.5846
9883.7984.758182.94986.56720.14710.96110.110.7015
9983.784.641282.65986.62330.1760.80.07740.6432
10083.7684.480382.28186.67950.26050.75660.18410.5743
10183.4784.538382.071687.00490.1980.73190.12760.5844
10283.7884.546581.852287.24080.28860.78320.17340.5797
10384.8384.553581.655687.45130.42580.69960.07140.576
10484.4384.463781.358987.56840.49150.40860.2730.5487
10584.984.379281.069987.68840.37890.4880.61850.5258
10685.3684.449280.944787.95380.30530.40050.28780.5399
10785.4984.428880.734588.12320.28670.31060.31250.5336
10885.2984.362180.481188.24310.31970.28450.51860.5186

\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[96]) \tabularnewline
84 & 85.65 & - & - & - & - & - & - & - \tabularnewline
85 & 85.74 & - & - & - & - & - & - & - \tabularnewline
86 & 85.89 & - & - & - & - & - & - & - \tabularnewline
87 & 86.08 & - & - & - & - & - & - & - \tabularnewline
88 & 85.49 & - & - & - & - & - & - & - \tabularnewline
89 & 85.97 & - & - & - & - & - & - & - \tabularnewline
90 & 85.84 & - & - & - & - & - & - & - \tabularnewline
91 & 86.72 & - & - & - & - & - & - & - \tabularnewline
92 & 85.42 & - & - & - & - & - & - & - \tabularnewline
93 & 83.87 & - & - & - & - & - & - & - \tabularnewline
94 & 85.45 & - & - & - & - & - & - & - \tabularnewline
95 & 85.35 & - & - & - & - & - & - & - \tabularnewline
96 & 84.27 & - & - & - & - & - & - & - \tabularnewline
97 & 83.13 & 84.4162 & 83.0751 & 85.7572 & 0.0301 & 0.5846 & 0.0265 & 0.5846 \tabularnewline
98 & 83.79 & 84.7581 & 82.949 & 86.5672 & 0.1471 & 0.9611 & 0.11 & 0.7015 \tabularnewline
99 & 83.7 & 84.6412 & 82.659 & 86.6233 & 0.176 & 0.8 & 0.0774 & 0.6432 \tabularnewline
100 & 83.76 & 84.4803 & 82.281 & 86.6795 & 0.2605 & 0.7566 & 0.1841 & 0.5743 \tabularnewline
101 & 83.47 & 84.5383 & 82.0716 & 87.0049 & 0.198 & 0.7319 & 0.1276 & 0.5844 \tabularnewline
102 & 83.78 & 84.5465 & 81.8522 & 87.2408 & 0.2886 & 0.7832 & 0.1734 & 0.5797 \tabularnewline
103 & 84.83 & 84.5535 & 81.6556 & 87.4513 & 0.4258 & 0.6996 & 0.0714 & 0.576 \tabularnewline
104 & 84.43 & 84.4637 & 81.3589 & 87.5684 & 0.4915 & 0.4086 & 0.273 & 0.5487 \tabularnewline
105 & 84.9 & 84.3792 & 81.0699 & 87.6884 & 0.3789 & 0.488 & 0.6185 & 0.5258 \tabularnewline
106 & 85.36 & 84.4492 & 80.9447 & 87.9538 & 0.3053 & 0.4005 & 0.2878 & 0.5399 \tabularnewline
107 & 85.49 & 84.4288 & 80.7345 & 88.1232 & 0.2867 & 0.3106 & 0.3125 & 0.5336 \tabularnewline
108 & 85.29 & 84.3621 & 80.4811 & 88.2431 & 0.3197 & 0.2845 & 0.5186 & 0.5186 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114669&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[96])[/C][/ROW]
[ROW][C]84[/C][C]85.65[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]85.74[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]85.89[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]87[/C][C]86.08[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]88[/C][C]85.49[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]89[/C][C]85.97[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]90[/C][C]85.84[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]91[/C][C]86.72[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]92[/C][C]85.42[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]93[/C][C]83.87[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]94[/C][C]85.45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]95[/C][C]85.35[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]96[/C][C]84.27[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]97[/C][C]83.13[/C][C]84.4162[/C][C]83.0751[/C][C]85.7572[/C][C]0.0301[/C][C]0.5846[/C][C]0.0265[/C][C]0.5846[/C][/ROW]
[ROW][C]98[/C][C]83.79[/C][C]84.7581[/C][C]82.949[/C][C]86.5672[/C][C]0.1471[/C][C]0.9611[/C][C]0.11[/C][C]0.7015[/C][/ROW]
[ROW][C]99[/C][C]83.7[/C][C]84.6412[/C][C]82.659[/C][C]86.6233[/C][C]0.176[/C][C]0.8[/C][C]0.0774[/C][C]0.6432[/C][/ROW]
[ROW][C]100[/C][C]83.76[/C][C]84.4803[/C][C]82.281[/C][C]86.6795[/C][C]0.2605[/C][C]0.7566[/C][C]0.1841[/C][C]0.5743[/C][/ROW]
[ROW][C]101[/C][C]83.47[/C][C]84.5383[/C][C]82.0716[/C][C]87.0049[/C][C]0.198[/C][C]0.7319[/C][C]0.1276[/C][C]0.5844[/C][/ROW]
[ROW][C]102[/C][C]83.78[/C][C]84.5465[/C][C]81.8522[/C][C]87.2408[/C][C]0.2886[/C][C]0.7832[/C][C]0.1734[/C][C]0.5797[/C][/ROW]
[ROW][C]103[/C][C]84.83[/C][C]84.5535[/C][C]81.6556[/C][C]87.4513[/C][C]0.4258[/C][C]0.6996[/C][C]0.0714[/C][C]0.576[/C][/ROW]
[ROW][C]104[/C][C]84.43[/C][C]84.4637[/C][C]81.3589[/C][C]87.5684[/C][C]0.4915[/C][C]0.4086[/C][C]0.273[/C][C]0.5487[/C][/ROW]
[ROW][C]105[/C][C]84.9[/C][C]84.3792[/C][C]81.0699[/C][C]87.6884[/C][C]0.3789[/C][C]0.488[/C][C]0.6185[/C][C]0.5258[/C][/ROW]
[ROW][C]106[/C][C]85.36[/C][C]84.4492[/C][C]80.9447[/C][C]87.9538[/C][C]0.3053[/C][C]0.4005[/C][C]0.2878[/C][C]0.5399[/C][/ROW]
[ROW][C]107[/C][C]85.49[/C][C]84.4288[/C][C]80.7345[/C][C]88.1232[/C][C]0.2867[/C][C]0.3106[/C][C]0.3125[/C][C]0.5336[/C][/ROW]
[ROW][C]108[/C][C]85.29[/C][C]84.3621[/C][C]80.4811[/C][C]88.2431[/C][C]0.3197[/C][C]0.2845[/C][C]0.5186[/C][C]0.5186[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114669&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[96])
8485.65-------
8585.74-------
8685.89-------
8786.08-------
8885.49-------
8985.97-------
9085.84-------
9186.72-------
9285.42-------
9383.87-------
9485.45-------
9585.35-------
9684.27-------
9783.1384.416283.075185.75720.03010.58460.02650.5846
9883.7984.758182.94986.56720.14710.96110.110.7015
9983.784.641282.65986.62330.1760.80.07740.6432
10083.7684.480382.28186.67950.26050.75660.18410.5743
10183.4784.538382.071687.00490.1980.73190.12760.5844
10283.7884.546581.852287.24080.28860.78320.17340.5797
10384.8384.553581.655687.45130.42580.69960.07140.576
10484.4384.463781.358987.56840.49150.40860.2730.5487
10584.984.379281.069987.68840.37890.4880.61850.5258
10685.3684.449280.944787.95380.30530.40050.28780.5399
10785.4984.428880.734588.12320.28670.31060.31250.5336
10885.2984.362180.481188.24310.31970.28450.51860.5186






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
970.0081-0.015201.654200
980.0109-0.01140.01330.93721.29571.1383
990.0119-0.01110.01260.88581.15911.0766
1000.0133-0.00850.01160.51880.9990.9995
1010.0149-0.01260.01181.14121.02741.0136
1020.0163-0.00910.01130.58750.95410.9768
1030.01750.00330.01020.07650.82870.9104
1040.0188-4e-040.0090.00110.72530.8516
1050.020.00620.00860.27120.67480.8215
1060.02120.01080.00890.82950.69030.8308
1070.02230.01260.00921.12610.72990.8544
1080.02350.0110.00930.8610.74080.8607

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
97 & 0.0081 & -0.0152 & 0 & 1.6542 & 0 & 0 \tabularnewline
98 & 0.0109 & -0.0114 & 0.0133 & 0.9372 & 1.2957 & 1.1383 \tabularnewline
99 & 0.0119 & -0.0111 & 0.0126 & 0.8858 & 1.1591 & 1.0766 \tabularnewline
100 & 0.0133 & -0.0085 & 0.0116 & 0.5188 & 0.999 & 0.9995 \tabularnewline
101 & 0.0149 & -0.0126 & 0.0118 & 1.1412 & 1.0274 & 1.0136 \tabularnewline
102 & 0.0163 & -0.0091 & 0.0113 & 0.5875 & 0.9541 & 0.9768 \tabularnewline
103 & 0.0175 & 0.0033 & 0.0102 & 0.0765 & 0.8287 & 0.9104 \tabularnewline
104 & 0.0188 & -4e-04 & 0.009 & 0.0011 & 0.7253 & 0.8516 \tabularnewline
105 & 0.02 & 0.0062 & 0.0086 & 0.2712 & 0.6748 & 0.8215 \tabularnewline
106 & 0.0212 & 0.0108 & 0.0089 & 0.8295 & 0.6903 & 0.8308 \tabularnewline
107 & 0.0223 & 0.0126 & 0.0092 & 1.1261 & 0.7299 & 0.8544 \tabularnewline
108 & 0.0235 & 0.011 & 0.0093 & 0.861 & 0.7408 & 0.8607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114669&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]97[/C][C]0.0081[/C][C]-0.0152[/C][C]0[/C][C]1.6542[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]98[/C][C]0.0109[/C][C]-0.0114[/C][C]0.0133[/C][C]0.9372[/C][C]1.2957[/C][C]1.1383[/C][/ROW]
[ROW][C]99[/C][C]0.0119[/C][C]-0.0111[/C][C]0.0126[/C][C]0.8858[/C][C]1.1591[/C][C]1.0766[/C][/ROW]
[ROW][C]100[/C][C]0.0133[/C][C]-0.0085[/C][C]0.0116[/C][C]0.5188[/C][C]0.999[/C][C]0.9995[/C][/ROW]
[ROW][C]101[/C][C]0.0149[/C][C]-0.0126[/C][C]0.0118[/C][C]1.1412[/C][C]1.0274[/C][C]1.0136[/C][/ROW]
[ROW][C]102[/C][C]0.0163[/C][C]-0.0091[/C][C]0.0113[/C][C]0.5875[/C][C]0.9541[/C][C]0.9768[/C][/ROW]
[ROW][C]103[/C][C]0.0175[/C][C]0.0033[/C][C]0.0102[/C][C]0.0765[/C][C]0.8287[/C][C]0.9104[/C][/ROW]
[ROW][C]104[/C][C]0.0188[/C][C]-4e-04[/C][C]0.009[/C][C]0.0011[/C][C]0.7253[/C][C]0.8516[/C][/ROW]
[ROW][C]105[/C][C]0.02[/C][C]0.0062[/C][C]0.0086[/C][C]0.2712[/C][C]0.6748[/C][C]0.8215[/C][/ROW]
[ROW][C]106[/C][C]0.0212[/C][C]0.0108[/C][C]0.0089[/C][C]0.8295[/C][C]0.6903[/C][C]0.8308[/C][/ROW]
[ROW][C]107[/C][C]0.0223[/C][C]0.0126[/C][C]0.0092[/C][C]1.1261[/C][C]0.7299[/C][C]0.8544[/C][/ROW]
[ROW][C]108[/C][C]0.0235[/C][C]0.011[/C][C]0.0093[/C][C]0.861[/C][C]0.7408[/C][C]0.8607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114669&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
970.0081-0.015201.654200
980.0109-0.01140.01330.93721.29571.1383
990.0119-0.01110.01260.88581.15911.0766
1000.0133-0.00850.01160.51880.9990.9995
1010.0149-0.01260.01181.14121.02741.0136
1020.0163-0.00910.01130.58750.95410.9768
1030.01750.00330.01020.07650.82870.9104
1040.0188-4e-040.0090.00110.72530.8516
1050.020.00620.00860.27120.67480.8215
1060.02120.01080.00890.82950.69030.8308
1070.02230.01260.00921.12610.72990.8544
1080.02350.0110.00930.8610.74080.8607


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; 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,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')