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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 computationSat, 25 Dec 2010 18:15:26 +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/25/t1293300781xgepyll0qga9dzb.htm/, Retrieved Sun, 28 Apr 2024 21:09:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115432, Retrieved Sun, 28 Apr 2024 21:09:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131

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 Forecasting...] [2010-12-06 13:02:50] [f4dc4aa51d65be851b8508203d9f6001]
-   PD        [ARIMA Forecasting] [ARIMA Forecasting...] [2010-12-19 20:46:40] [f4dc4aa51d65be851b8508203d9f6001]
-    D          [ARIMA Forecasting] [ARIMA FORECAST] [2010-12-25 16:51:28] [f9eaed74daea918f73b9f505c5b1f19e]
-    D              [ARIMA Forecasting] [Arima forecasting...] [2010-12-25 18:15:26] [2e49bff66bb3e1f5d7fa8957e12fbb12] [Current]
-   P                 [ARIMA Forecasting] [Arima forecasting...] [2010-12-25 18:35:08] [f9eaed74daea918f73b9f505c5b1f19e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
25.22
27.63
27.47
22.54
27.4
29.68
28.51
29.89
32.62
30.93
32.52
25.28
25.64
27.41
24.4
25.55
28.45
27.72
24.54
25.67
25.54
20.48
18.94
18.6
19.49
20.29
23.69
25.65
25.43
24.13
25.77
26.63
28.34
27.55
24.5
28.52
31.29
32.65
30.34
25.02
25.81
27.55
28.4
29.83
27.1
29.59
28.77
29.88
31.18
30.87
33.8
33.36
37.92
35.19
38.37
43.03
43.38
49.77
43.05
39.65
44.28
45.56
53.08
51.86
48.67
54.31
57.58
64.09
62.98
58.52
55.54
56.75
63.57
59.92
62.25
70.44
70.19
68.86
73.9
73.61
62.77
58.38
58.48
62.31
54.3
57.76
62.14
67.4
67.48
71.32
77.2
70.8
77.13
83.04
92.53
91.45
91.92
94.82
103.28
110.44
123.94
133.05
133.9
113.85
99.06
72.84
53.24
41.58
44.86
43.24
46.84
50.85
57.94
68.59
64.92
72.5
67.69
73.19
77.04
74.67

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115432&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115432&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'RServer@AstonUniversity' @ vre.aston.ac.uk






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[108])
9691.45-------
9791.92-------
9894.82-------
99103.28-------
100110.44-------
101123.94-------
102133.05-------
103133.9-------
104113.85-------
10599.06-------
10672.84-------
10753.24-------
10841.58-------
10944.8634.494723.519445.470.03210.102900.1029
11043.2431.584312.511450.65710.11550.086200.1522
11146.8433.9317.417160.44480.170.245700.2859
11250.8536.67483.381669.96810.2020.274800.3864
11357.9440.3720.91179.83290.19140.301400.4761
11468.5943.919-1.173689.01170.14180.27111e-040.5405
11564.9246.4256-3.840396.69140.23540.19373e-040.5749
11672.539.1376-15.912894.1880.11750.17930.00390.4654
11767.6933.7475-25.758393.25330.13180.10090.01570.3982
11873.1925.4675-38.213989.14880.07090.09690.07240.31
11977.0420.099-47.518487.71630.04940.06190.16840.2668
12074.6716.4111-54.935787.75780.05470.04790.24460.2446

\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[108]) \tabularnewline
96 & 91.45 & - & - & - & - & - & - & - \tabularnewline
97 & 91.92 & - & - & - & - & - & - & - \tabularnewline
98 & 94.82 & - & - & - & - & - & - & - \tabularnewline
99 & 103.28 & - & - & - & - & - & - & - \tabularnewline
100 & 110.44 & - & - & - & - & - & - & - \tabularnewline
101 & 123.94 & - & - & - & - & - & - & - \tabularnewline
102 & 133.05 & - & - & - & - & - & - & - \tabularnewline
103 & 133.9 & - & - & - & - & - & - & - \tabularnewline
104 & 113.85 & - & - & - & - & - & - & - \tabularnewline
105 & 99.06 & - & - & - & - & - & - & - \tabularnewline
106 & 72.84 & - & - & - & - & - & - & - \tabularnewline
107 & 53.24 & - & - & - & - & - & - & - \tabularnewline
108 & 41.58 & - & - & - & - & - & - & - \tabularnewline
109 & 44.86 & 34.4947 & 23.5194 & 45.47 & 0.0321 & 0.1029 & 0 & 0.1029 \tabularnewline
110 & 43.24 & 31.5843 & 12.5114 & 50.6571 & 0.1155 & 0.0862 & 0 & 0.1522 \tabularnewline
111 & 46.84 & 33.931 & 7.4171 & 60.4448 & 0.17 & 0.2457 & 0 & 0.2859 \tabularnewline
112 & 50.85 & 36.6748 & 3.3816 & 69.9681 & 0.202 & 0.2748 & 0 & 0.3864 \tabularnewline
113 & 57.94 & 40.372 & 0.911 & 79.8329 & 0.1914 & 0.3014 & 0 & 0.4761 \tabularnewline
114 & 68.59 & 43.919 & -1.1736 & 89.0117 & 0.1418 & 0.2711 & 1e-04 & 0.5405 \tabularnewline
115 & 64.92 & 46.4256 & -3.8403 & 96.6914 & 0.2354 & 0.1937 & 3e-04 & 0.5749 \tabularnewline
116 & 72.5 & 39.1376 & -15.9128 & 94.188 & 0.1175 & 0.1793 & 0.0039 & 0.4654 \tabularnewline
117 & 67.69 & 33.7475 & -25.7583 & 93.2533 & 0.1318 & 0.1009 & 0.0157 & 0.3982 \tabularnewline
118 & 73.19 & 25.4675 & -38.2139 & 89.1488 & 0.0709 & 0.0969 & 0.0724 & 0.31 \tabularnewline
119 & 77.04 & 20.099 & -47.5184 & 87.7163 & 0.0494 & 0.0619 & 0.1684 & 0.2668 \tabularnewline
120 & 74.67 & 16.4111 & -54.9357 & 87.7578 & 0.0547 & 0.0479 & 0.2446 & 0.2446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115432&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[108])[/C][/ROW]
[ROW][C]96[/C][C]91.45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]97[/C][C]91.92[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]98[/C][C]94.82[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]99[/C][C]103.28[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]100[/C][C]110.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]101[/C][C]123.94[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]102[/C][C]133.05[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]103[/C][C]133.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]104[/C][C]113.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]105[/C][C]99.06[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]106[/C][C]72.84[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]107[/C][C]53.24[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]108[/C][C]41.58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]109[/C][C]44.86[/C][C]34.4947[/C][C]23.5194[/C][C]45.47[/C][C]0.0321[/C][C]0.1029[/C][C]0[/C][C]0.1029[/C][/ROW]
[ROW][C]110[/C][C]43.24[/C][C]31.5843[/C][C]12.5114[/C][C]50.6571[/C][C]0.1155[/C][C]0.0862[/C][C]0[/C][C]0.1522[/C][/ROW]
[ROW][C]111[/C][C]46.84[/C][C]33.931[/C][C]7.4171[/C][C]60.4448[/C][C]0.17[/C][C]0.2457[/C][C]0[/C][C]0.2859[/C][/ROW]
[ROW][C]112[/C][C]50.85[/C][C]36.6748[/C][C]3.3816[/C][C]69.9681[/C][C]0.202[/C][C]0.2748[/C][C]0[/C][C]0.3864[/C][/ROW]
[ROW][C]113[/C][C]57.94[/C][C]40.372[/C][C]0.911[/C][C]79.8329[/C][C]0.1914[/C][C]0.3014[/C][C]0[/C][C]0.4761[/C][/ROW]
[ROW][C]114[/C][C]68.59[/C][C]43.919[/C][C]-1.1736[/C][C]89.0117[/C][C]0.1418[/C][C]0.2711[/C][C]1e-04[/C][C]0.5405[/C][/ROW]
[ROW][C]115[/C][C]64.92[/C][C]46.4256[/C][C]-3.8403[/C][C]96.6914[/C][C]0.2354[/C][C]0.1937[/C][C]3e-04[/C][C]0.5749[/C][/ROW]
[ROW][C]116[/C][C]72.5[/C][C]39.1376[/C][C]-15.9128[/C][C]94.188[/C][C]0.1175[/C][C]0.1793[/C][C]0.0039[/C][C]0.4654[/C][/ROW]
[ROW][C]117[/C][C]67.69[/C][C]33.7475[/C][C]-25.7583[/C][C]93.2533[/C][C]0.1318[/C][C]0.1009[/C][C]0.0157[/C][C]0.3982[/C][/ROW]
[ROW][C]118[/C][C]73.19[/C][C]25.4675[/C][C]-38.2139[/C][C]89.1488[/C][C]0.0709[/C][C]0.0969[/C][C]0.0724[/C][C]0.31[/C][/ROW]
[ROW][C]119[/C][C]77.04[/C][C]20.099[/C][C]-47.5184[/C][C]87.7163[/C][C]0.0494[/C][C]0.0619[/C][C]0.1684[/C][C]0.2668[/C][/ROW]
[ROW][C]120[/C][C]74.67[/C][C]16.4111[/C][C]-54.9357[/C][C]87.7578[/C][C]0.0547[/C][C]0.0479[/C][C]0.2446[/C][C]0.2446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115432&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[108])
9691.45-------
9791.92-------
9894.82-------
99103.28-------
100110.44-------
101123.94-------
102133.05-------
103133.9-------
104113.85-------
10599.06-------
10672.84-------
10753.24-------
10841.58-------
10944.8634.494723.519445.470.03210.102900.1029
11043.2431.584312.511450.65710.11550.086200.1522
11146.8433.9317.417160.44480.170.245700.2859
11250.8536.67483.381669.96810.2020.274800.3864
11357.9440.3720.91179.83290.19140.301400.4761
11468.5943.919-1.173689.01170.14180.27111e-040.5405
11564.9246.4256-3.840396.69140.23540.19373e-040.5749
11672.539.1376-15.912894.1880.11750.17930.00390.4654
11767.6933.7475-25.758393.25330.13180.10090.01570.3982
11873.1925.4675-38.213989.14880.07090.09690.07240.31
11977.0420.099-47.518487.71630.04940.06190.16840.2668
12074.6716.4111-54.935787.75780.05470.04790.24460.2446






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
1090.16230.30050107.439500
1100.30810.3690.3348135.8565121.64811.0294
1110.39870.38040.35166.6427136.646211.6896
1120.46320.38650.3591200.936152.718612.3579
1130.49870.43520.3743308.636183.902113.5611
1140.52380.56170.4056608.6567254.694515.9592
1150.55240.39840.4045342.044267.17316.3454
1160.71760.85240.46051113.0521372.907919.3108
1170.89961.00580.52111152.0943459.484221.4356
1181.27581.87390.65642277.4379641.279625.3235
1191.71642.8330.85433242.2796877.734129.6266
1202.21813.551.07893394.1051087.431732.9762

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
109 & 0.1623 & 0.3005 & 0 & 107.4395 & 0 & 0 \tabularnewline
110 & 0.3081 & 0.369 & 0.3348 & 135.8565 & 121.648 & 11.0294 \tabularnewline
111 & 0.3987 & 0.3804 & 0.35 & 166.6427 & 136.6462 & 11.6896 \tabularnewline
112 & 0.4632 & 0.3865 & 0.3591 & 200.936 & 152.7186 & 12.3579 \tabularnewline
113 & 0.4987 & 0.4352 & 0.3743 & 308.636 & 183.9021 & 13.5611 \tabularnewline
114 & 0.5238 & 0.5617 & 0.4056 & 608.6567 & 254.6945 & 15.9592 \tabularnewline
115 & 0.5524 & 0.3984 & 0.4045 & 342.044 & 267.173 & 16.3454 \tabularnewline
116 & 0.7176 & 0.8524 & 0.4605 & 1113.0521 & 372.9079 & 19.3108 \tabularnewline
117 & 0.8996 & 1.0058 & 0.5211 & 1152.0943 & 459.4842 & 21.4356 \tabularnewline
118 & 1.2758 & 1.8739 & 0.6564 & 2277.4379 & 641.2796 & 25.3235 \tabularnewline
119 & 1.7164 & 2.833 & 0.8543 & 3242.2796 & 877.7341 & 29.6266 \tabularnewline
120 & 2.2181 & 3.55 & 1.0789 & 3394.105 & 1087.4317 & 32.9762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115432&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]109[/C][C]0.1623[/C][C]0.3005[/C][C]0[/C][C]107.4395[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]110[/C][C]0.3081[/C][C]0.369[/C][C]0.3348[/C][C]135.8565[/C][C]121.648[/C][C]11.0294[/C][/ROW]
[ROW][C]111[/C][C]0.3987[/C][C]0.3804[/C][C]0.35[/C][C]166.6427[/C][C]136.6462[/C][C]11.6896[/C][/ROW]
[ROW][C]112[/C][C]0.4632[/C][C]0.3865[/C][C]0.3591[/C][C]200.936[/C][C]152.7186[/C][C]12.3579[/C][/ROW]
[ROW][C]113[/C][C]0.4987[/C][C]0.4352[/C][C]0.3743[/C][C]308.636[/C][C]183.9021[/C][C]13.5611[/C][/ROW]
[ROW][C]114[/C][C]0.5238[/C][C]0.5617[/C][C]0.4056[/C][C]608.6567[/C][C]254.6945[/C][C]15.9592[/C][/ROW]
[ROW][C]115[/C][C]0.5524[/C][C]0.3984[/C][C]0.4045[/C][C]342.044[/C][C]267.173[/C][C]16.3454[/C][/ROW]
[ROW][C]116[/C][C]0.7176[/C][C]0.8524[/C][C]0.4605[/C][C]1113.0521[/C][C]372.9079[/C][C]19.3108[/C][/ROW]
[ROW][C]117[/C][C]0.8996[/C][C]1.0058[/C][C]0.5211[/C][C]1152.0943[/C][C]459.4842[/C][C]21.4356[/C][/ROW]
[ROW][C]118[/C][C]1.2758[/C][C]1.8739[/C][C]0.6564[/C][C]2277.4379[/C][C]641.2796[/C][C]25.3235[/C][/ROW]
[ROW][C]119[/C][C]1.7164[/C][C]2.833[/C][C]0.8543[/C][C]3242.2796[/C][C]877.7341[/C][C]29.6266[/C][/ROW]
[ROW][C]120[/C][C]2.2181[/C][C]3.55[/C][C]1.0789[/C][C]3394.105[/C][C]1087.4317[/C][C]32.9762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115432&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
1090.16230.30050107.439500
1100.30810.3690.3348135.8565121.64811.0294
1110.39870.38040.35166.6427136.646211.6896
1120.46320.38650.3591200.936152.718612.3579
1130.49870.43520.3743308.636183.902113.5611
1140.52380.56170.4056608.6567254.694515.9592
1150.55240.39840.4045342.044267.17316.3454
1160.71760.85240.46051113.0521372.907919.3108
1170.89961.00580.52111152.0943459.484221.4356
1181.27581.87390.65642277.4379641.279625.3235
1191.71642.8330.85433242.2796877.734129.6266
1202.21813.551.07893394.1051087.431732.9762


Figures (Output of Computation)

Input Parameters & R Code

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